Let A be a \C-algebra with an action of finite group G, let $\natural$ 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine Hochschild homology [G,\natural]$ for two classes algebras A: - rings regular functions nonsingular affine varieties, graded Hecke algebras. The results are achieved via algebraic families (virtual) representations include des...

In this paper, we re-examine certain integrable modules of Chari-Presslely for an (untwisted) affine Lie algebra ĝ by exploiting basic formal variable techniques. We define and study two categories E and C of ĝ-modules using generating functions, where E contains evaluation modules and C unifies highest weight modules, evaluation modules and their tensor product modules, and we classify integra...

Rogers-Ramanujan type partition identities establish equalities between certain types of partitions with difference conditions and partitions whose generating functions is an infinite product. Since the 1980’s, many connections between representations of Lie algebras and RogersRamanujan type partition identities have emerged. Lepowsky and Wilson [6] were the first to establish this link by givi...

in this paper, an observer based fuzzy adaptive controller (fac) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. it isassumed that functions of the subsystems and the interactions among subsystems areunknown. by constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured sta...

This paper is concerned with the problem of Boolean approximation in the following sense: given a Boolean function class and an arbitrary Boolean function, what is the function’s best proxy in the class? Specifically, what is its strongest logical consequence (or envelope) in the class of affine Boolean functions. We prove various properties of affine Boolean functions and their representation ...