Cohomology of restricted Lie–Rinehart algebras and the Brauer group

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

Module cohomology group of inverse semigroup algebras

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

Cohomology of Restricted Lie Algebras

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. Motivations for the definition of a restricted Lie algebra are given and the theory of ordinary Lie algebra cohomology is briefly reviewed, including a discussion on algebraic interpretations of the low dimensional cohomology spaces of ordinary Lie algebras. The general Cartan-Eilenberg construction of the st...

The symmetric group and Brauer algebras

The Cohomology of Restricted Lie Algebras and of Hopf Algebras

Introduction. In theory, the bar construction suffices to calculate the homology groups of an augmented algebra. In practice, the bar construction is generally too large (has too many generators) to allow computation of higher-dimensional homology groups. In this paper, we outline a procedure which simplifies the calculation of the homology and cohomology of Hopf algebras. Let i b e a (graded) ...