6/26 (Tue) 
6/27 (Wed) 
6/28 (Thu) 
6/29 (Fri) 
6/30 (Sat) 
7/1 (Sum) 

08:30¡X09:15 

09:45¡X10:30 

11:00¡X11:45 

14:00¡X14:45 

15:15¡X16:00 

16:30¡X17:15 

Evening 
B.B.Q. 
Banquet 
Back to the Poster Page 
Abstracts 
June 26 
08:30¡X09:15 
From PSp(4,3) to the Monster 

09:45¡X10:30 
Crystal bases for quantum affine algebras and combinatorics of Young walls 

11:00¡X11:45 
Units of twisted group algebras 

14:00¡X14:45 
Codes, Moonshine VOA, and Monster 

15:15¡X16:00 
Local theta correspondence and minimal Ktypes of positive depth 

16:30¡X17:15 
Hecke algebras, Specht modules and GröbnerShirshov bases 

June 27 
08:30¡X09:15 
Algebraic methods in measure theory 

09:45¡X10:30 
An improved version of standard bases 

11:00¡X11:45 
Polynomials and Polynomial Functions 

14:00¡X14:45 
Recent progress in the structure of division algebras 

15:15¡X16:00 
Symmetric quantum Lie operations and differential calculi 

16:30¡X17:15 

June 28 
08:30¡X09:15 
Lie algebras over noncommutative rings and pseudoalgebras 

09:45¡X10:30 
From Jacobson rings to the Jacobson conjecture 

11:00¡X11:45 
On functional identities and their applications 

14:00¡X14:45 
On some problems in PITheory in characteristic p 

15:15¡X16:00 
Primitive elements of free algebras of Schreier varieties 

16:30¡X17:15 

June 29 
Sight seeing tour 

June 30 
08:30¡X09:15 
Lattices in KacMoody groups 

09:45¡X10:30 
Represention theory of the super W_{1+}_{¡Û} and its subalgebras 

11:00¡X11:45 
Orders in simple algebras 

14:00¡X14:45 
On Amendariz rings 

15:15¡X16:00 
Homological properties of PI Hopf algebras 

16:30¡X17:15 
Cancellation for curves 

July 1 
08:30¡X09:15 
GröbnerShirshov bases for algebras and groups 

09:45¡X10:30 
Derivations in prime rings 

11:00¡X11:45 
Skew derivations algebraic over prime rings 

14:00¡X14:45 

15:15¡X16:00 

16:30¡X17:15 
l On functional identities and their applications
K. I. Beidar
Let R be a field, let S be a nonempty set, let £\ : S ¡÷ R be a map and let 0 ¡Ú f(x_{1}, x_{2}, ¡K, x_{n+1}) £` R[x_{1}, x_{2}, ¡K, x_{n+1}]. Recall that a function £p : S^{n} ¡÷ R is called algebraic if
f(x_{1}^{£\}, x_{2}^{£\}, ¡K, x_{n}^{£\},£p(x_{1}, x_{2}, ¡K, x_{n})) = 0
for all x_{1}, x_{2}, ¡K, x_{n }£` S. Now assume that deg_{x_{n+1}}(f) = 1. Then one can find £p from the above equation. Therefore one can find explicitly algebraic functions of degree 1. It happens that an analogous result is true (under mild assumptions on Im(£\) and £p) in the case when R is a noncommutative ring and f is a polynomial in noncommutative variables.
In the talk we shall discuss recent results on functional identities and their applications. Loosely speaking the theory of functional identities is the theory of ¡§algebraic functions of degree 1¡¨ in noncommutative rings. Functional identities were the main tool in solutions of long standing Herstein's problems on Lie and Jordan maps in noncommutative rings. They have applications to Lieadmissible algebras, graded polynomial identities and theory of linear preservers.
L. A. Bokut
A.I. Shirshov (1962) invented a new general method of dealing with defining relations of any Lie algebra. Shirshov's method was explicitly formulated by the author in 1972 and then extended to associative algebras in 1976. Essentially, the same method for commutative algebras was discovered in a paper by H. Hironaka in 1964 and in a Thesis by B. Buchberger in 1965, under supervisions of W. Gröbner (published in 1970). Also G. Bergman in 1978 published some similar results for associative algebras. Later on the Sirshov method had been called the GröbnerShirshov bases method for noncommutative and Lie algebras.
Recently the GröbnerShirshov bases method had been extended to conformal algebras by the author, Y. Fong and W.F. Ke. Also a general hypothesis was formulated for GröbnerShirshov bases of any Coxeter group joint with L.S. Shiao. This hypothesis is proved for the Coxeter groups of the types A_{n}, B_{n}, D_{n}, as well as for some others cases.
Mikhail Chebotar
We shall briefly survey several topics on derivations in prime rings. In particular, solutions of Herstein's problems on Lie derivations (joint work with K. I. Beidar, M. Brešar and W. S. Martindale) and Lanski's problems on compositions of derivations (joint work with P.H. Lee) will be presented.
l Representation theory of the super W_{1+}_{¡Û} and its subalgebras
S.J. Cheng
We study quasifinite representations of the Lie superalgebra of differential operators on the circle with N=1 extended symmetry, the socalled super W_{1+}_{¡Û}, from the perspective of Howe duality. In particular we obtain a duality, in the sense of Howe, between super W_{1}_{+}_{¡Û} and the general linear group GL(n). We also exhibit a duality between a Btype subalgebra of the super W_{1}_{+}_{¡Û} and Pin(2n).
Koichiro Harada
A (general) curve of degree 3 contains exactly 27 lines and the automorphism group of its configuration is PSp(4,3). Firstly a 3 x 3 matrix having (1,1) entry PSp(4,3) and (3,3) entry Monster is defined and its meaning is explored. Secondly the characterization of Sylow 2subgroups of finite simple groups is discussed.
SeokJin Kang
We give a realization of crystal bases for quantum affine algebras using some new combinatorial objects which we call the Young walls. The Young walls consist of colored blocks with various shapes that are built on the given groundstate wall and can be viewed as generalizations of Young diagrams. The rules for building Young walls and the action of Kashiwara operators are given explicitly in terms of combinatorics of Young walls. The characters of of basic representations can be computed easily by counting the number of colored blocks that have been added to the groundstate wall.
l On some problems in PITheory in characteristic p
Alexander Kemer
We'll talk about some old and new results about the identities of PIalgebras over a field of characteristic p. Most of theresults are concerning the prime varieties.
V.K. Kharchenko
The notion of quantum Lie operation naturally appeared in line with the Friedrichs criteria for Lie polynomials (Journal of Algebra, 217, 188228, 1999). We prove that the (n  2)!dimensional space of generic quantum Lie operations has a basis of the symmetric ones. In the general case almost always a basis of symmetric operations exists. All exceptional cases are found. We propose a notion of a quantum universal enveloping algebra based on the quantum Lie operation concept. This enveloping algebra has PBW basis that admits a monomial crystallization. Every homogeneous character Hopf algebra over a field of zero characteristic is a quantum universal enveloping algebra of a suitable Lie algebra. We investigate in details a left covariant first order differential calculus that naturally arises on each skew primitively generated Hopf algebra with a week homogeneity condition. By means of the P. M. Cohn theory we show that the subalgebra of constants for the cover free differential algebra is a free algebra and an adinvariant left coideal. We prove density and structural theorems for the operator algebra generated by partial derivatives. If the given algebra is finitely generated then every differential left ideal is generated by constants, a noncommutative Tailor series decomposition formula is valid, and the category of locally nilpotent modules over the operator algebra is semisimple with the only simple object that is isomorphic to the optimal algebra as a module. We find a necessary and sufficient condition for a 1form to be a complete differential.
C.H. Lam
Victor N. Latyshev
In order to extend the area of applications a comprehensive idea of standard bases is introduced in weak restrictions on simplifications. The wellknown examples and new instances are described from a general point of view, and some recognizable properties of associative algebras are presented.
l Hecke algebras, Specht modules and GröbnerShirshov bases
K. H. Lee
I will talk about GrobnerShirshov bases for Specht modules of Hecke algebras of type A. The structure of Specht modules will be explained using the combinatorics of Young walls. As an application, an algorithm of computing Gram matrices will be discussed.
l Skew derivations algebraic over prime rings
T.K. Lee
Let R be a prime ring with extended centroid C and left Martindale quotient ring R_{{\cal F}}. In this paper we first give a characterization of £mderivations which are left algebraic over R_{{\cal F}} modulo finitedimensional subspaces of R_{{\cal F}}. Applying this characterization we prove some results concerning £mderivations. This is a joint paper with Professor ChenLian Chuang.
l Units of twisted group algebras
ChiaHsin Liu
Let U be the group of units of a twisted group algebra. We are interested in the following two problems:
1. When does U satisfy a group identity?
2. When does U contain a free subgroup of rank two?
L. MakarLimanov
Here is the cancellation theorem of AbhyankarEakinHeinzer, see S. Abhyankar, P. Eakin, W. Heinzer, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310342.
Let £F_{1} and £F_{2} be two curves and O(£F_{1}), O(£F_{2}) be the rings of regular functions on £F_{1} and £F_{2}. If O(£F_{1})[x_{1}, ..., x_{n}] \IsomorphicTo O(£F_{2})[x_{1}, ..., x_{n}], then O(£F_{1}) \IsomorphicTo O(£F_{2}).
In the talk a new proof of this theorem in the case of characteristic zero which is based on the computations of invariant \AK and some conjectures will be discussed.
l Primitive Elements of Free Algebras of Schreier Varieties
Alexander A. Mikhalev
We expose results on primitive elements of free algebras of main types of Schreier varieties of algebras. A variety of linear algebras over a field is Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras. A system of elements of a free algebra is primitive if it is a subset of some set of free generators of this algebra. We consider free nonassociative algebras, free commutative and anticommutative nonassociative algebras, free Lie algebras and superalgebras, free Lie palgebras and psuperalgebras. We present matrix criteria for systems of elements to be primitive. It gives a possibility to obtain algorithms to recognize primitive systems of elements. Primitive elements distinguish automorphisms: endomorphisms sending primitive elements to primitive elements are automorphisms. Finally, we consider stable and dense properties for primitive elements.
Alexander V. Mikhalev
The following new algebraic lines in measure theory (developed recently by A. V. Mikhalev and V. K. Zakharov) are under consideration:
1. Radon measures and bimeasures.
2. Rings and modules related to measure theory.
3. Thin linear functionals and metasemicontinuous functions.
4. Integral representation for Radon (bi)measures over an arbitrary Hausdorff space (a solution of RieszRadon problem)
l Lcal theta correspondence and minimal Ktypes of positive depth
S.Y. Pan
In this talk, we want to discuss the relation between the minimal Ktypes of the irreducible admissible representations paired by theta correspondence. In particular, we show that the minimal Ktypes are paired by orbit correspondence when the depth is positive.
G. Pilz
Polynomials over rings are pretty wellknown. What about polynomials over general algebraic structures? Even if we stay in the case of rings: what is the relation to polynomial functions, can we always ¡§compare coefficients¡¨? What you always wanted to know abut commuting and/or noncommuting variables, but never dared to ask. Why are polynomials so useful for describing ideals in Omegagroups? For the description of the structure of universal algebras via commutators? Every polynomial map is ¡§compatible¡¨: it maps congruent elements into congruent ones. When is every map on an algebra a polynomial map (polynomial completeness)? When is every compatible function a polynomial one (affine completeness)?
L. Rowen
The major question in the structure theory of division algebras may be to express a given Fdivision algebra D in terms of cyclic algebras. Although the MerkurjevSuslin Theorem says that (assuming F has enough roots of 1) some matrix ring M_{t}(D) is isomorphic to a tensor product of cyclic algebras, no bound is given on t. Indeed it has long been known t = 1 for D of degree 2, 3, and 6, and t > 1 if deg (D) is divisible by a square number > 1. On the other hand, it is unknown whether or not t = 1 for deg(D) squarefree. Our main result (jointly with Lorenz, Reichstein, and Saltman) is that if deg(D) = 4 then t = 2, i.e. M_{2}(D) is similar to a tensor product of two cyclic algebras, of respective degrees 4 and 2. The proof relies on earlier structural results of Albert, AmitsurSaltman, and Tignol. The theorem can be seen in a broader context using the essential dimension, and I will describe what is known about the essential dimension of central simple algebras.
l From Jacobson Rings to the Jacobson Conjecture
Lance W. Small
I'll give a survey of the results and background of the Jacobson Conjecture and, then, relate it recent developments in affine algebras.
l Applications of combinatorial algebra to cryptography
V. Shpilrain
This talk will focus on recent applications of algebra to cryptography. This area is becoming increasingly popular because most of the presently existing computer security systems
are becoming outdated due to a dramatic increase in the speed of computation offered by modern computers. There is therefore a high demand for brand new ideas in this area. We are going to survey some of them.
TsaiLien Wong
A ring R is called Armendariz if whenever polynomials f(X) = a_{0} + a_{1}X + ¡K + a_{m}X^{m} and g(X) = b_{0} + b_{1}X + ¡K+ b_{n}X^{n} in R[X] satisfy f(X)g(X) = 0, then a_{i}b_{j} = 0 for all i, j. A ring R is called reduced if it has no nonzero nilpotent elements. The study of Armendariz rings was initiated by Armendariz, Rege and Chhawchharia.
In this talk we are concerned with the connections among (weak) Armendariz rings, reduced rings and semiprime right Goldie rings. We construct certain Armendariz rings and prove that a semiprime right Goldie ring is weak Armendariz if and only if it is a reduced ring.
E. Zelmanov
l Homological properties of PI Hopf algebras
J. Zhang
Quantum groups at the roots of unity form a family of noetherian PI Hopf algebra. This family of algebras have nice homological properties such as the AuslanderBuchsbaum formula, Bass theorem, and the Gorenstein property. The talk will review some results of Brown and Goodearl and some recent work of Wu by using the noncommutative version of dualizing complexes introduced by Yekutieli.