北京师范大学数学科学学院教育部“数学与复杂系统”重点实验室代数年活动之一：代数与表示论会议，2014年6月14-15日。
会议程序
注：北京师范大学新主楼1124报告厅。
报告题目与摘要：
邓邦明（清华大学）：Simple representations of affine q-Schur algebras
In this talk I will explain how to identify simple representations of affine q-Schur algebras arising from simple polynomial representations of quantum affine gl_n with those arising from simple modules of affine Hecke algebras of type A. This is based on joint work with Jie Du and Qiang Fu.
郭向前（郑州大学）：Jet modules for the Virasoro-like algebra
In this talk, we studied the jet modules for the Virasoro-like algebra, one of the infinite dimensional Lie algebras with simplest structure. The jet modules are certain natural modules over the Lie algebra of semi-direct product of the Virasoro-like algebra and the Laurent polynomials in two variables. We show that the jet modulesare polynomial modules. Then we characterize the irreducible (resp. indecomposable) jet modules with finite dimensional modules over sl_2 (resp. B'_+, which is the "positive part" of a Block type algebra).
韩阳（中国科学院）：Hochschild homology dimension conjecture: 1 decade
In this talk, I shall tell a tale on the Hochschild homology dimension conjecture, which includes some results, approaches, thoughts, questions, and so on.
刘品（西南交通大学）：On Tau-tilting Modules
Tau-tilting is a recent, important development in tilting theory where tilting modules are replaced by so-called tau-tilting modules. In this talk, we review the foundations and report on recent work.
潘升勇（北京交通大学）：Derived equivalences for \Phi-Cohen–Macaulay Auslander–Yoneda algebras
In this paper, we introduce a class of algebras called \Phi-Cohen–Macaulay Auslander–Yoneda algebras with \Phi an admissible set of N, and construct derived equivalences between these \Phi-Cohen–Macaulay Auslander–Yoneda algebras from a given derived equivalence.
王立中（北京大学）：Orbital characters and their applications
In this talk, we provide some formulae to calculate orbital characters. Some elementary properties about orbital characters are also included. Especially we give a lifting theorem by which one can read off the value of orbital characters from local subgroups. With orbital characters, we can show that Reynolds ideal is dual to the vector space of simple modules and this leads to a new method to count simple modules. Some other applications to modular representation are also included.
惠昌常（首都师范大学）：Recollements of derived categories induced from exact contexts
We shall present a general context to construct recollements of derived module categories of rings by introducing exact contexts which are a far-reaching generalization of pullbacks of rings and can be obtained easily from rigid morphisms.
The contents of the talk are taken from a joint work “Recollements of derived categories I: exact contexts” with H. X. Chen, which can be downloaded from: http://math.bnu.edu.cn/_ccxi/2012Test/Engindex.html.
徐帆（清华大学）：From Hall algebras to cluster algebras
In this talk, we present the constructions Hall algebras of some orbit triangulated categories via derived Hall algebras for derived categories and characterize relations between them. As an application, we construct a natural algebra homomorphism from the Ringel-Hall algebra of a hereditary algebra to the corresponding quantum cluster algebra. This gives alternative proofs of some results recently obtained by Berensein and Rupel. This is a talk on joint work with Ding Ming.
徐运阁（湖北大学）：Hochschild cohomology ring of tame Hecke algebras
Let A be a tame Hecke algebra of type A. Based on the minimal projective bimodule resolution (P,) of A constructed by Schroll and Snashall, we first give an explicit description of the so-called ``comultiplicative structure" of the generators of each term
in (P,
), and then apply it to define a chain map
and thus show that the cup product in the level of cochains for the tame Hecke algebra A is essentially juxtaposition of parallel paths up to sign. As a consequence, we determine the structure of the Hochschild cohomology ring of A under the cup product by give an explicit presentation by generators and relations.
张红莲（上海大学）：Hopf algebraic structures of quantum affine algebra and quantum toroidal algebra
In this talk, we construct a new set of simpler generators of quantum affine algebras to replace the original full set of the generators, and this also enables us to give a Hopf algebraic structure for the Drinfeld realization of the quantum affine algebras. Furthermore, we study the Hopf algebraic structure of quantum toroidal algebra for type A. It should be pointed out that this method works well for both one-parameter case and two-parameter case. The talk is based on the joint work with Prof. Naihuan Jing.
赵中华（北京化工大学）：Global bases of U_q(g)-modules over quantum generalized Kac-Moody algebras and some applications
We deal with the matrix coefficients of e_i and f_i on global crystal bases. Based on the analysis of matrix coefficients, we consider the global bases of U_q^+(g)-modules and give some applications.
周国栋（华东师范大学）：Two applications of the resolution theorem
Resolution Theorem is one of the basic results in Quillen's algebraic K-theory. We present a folklore version of this theorem for derived categories. We apply it to monomorphism categories and vector bundles over an elliptic curve.
周远洋（华中师范大学）：K-stable splendid Rickard complexes
In this paper, Broue's conjecture is reduced to simple groups with a stability condition.
朱灿（上海理工大学）：Homological Determinant
A finite subgroup of SL(n, k) can freely act on the polynomial ring over a field k with n variables. We will firstly recall some results on this action and its' invariant, such as McKay correspondence, Watanabe's Theorem, Shephard-Todd-Chevalley Theorem etc. In order to generalize these to noncommutative setting, one needs to generalize the determinant of a matrix to noncommutative setting. Jorsengen and Zhang propose the notion of homological determinant. Secondly, we will give a survey on noncommutative action and its' invariant recent years.
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