An almost para-CR structure on a manifold M is given by a distribution HM ⊂ TM together with a field K ∈ Γ(End(HM)) of involutive endomorphisms of HM . If K satisfies an integrability condition, then (HM,K) is called a para-CR structure. The notion of maximally homogeneous para-CR structure of a semisimple type is given. A classification of such maximally homogeneous para-CR structures is given...

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we Rees matrix semigroups, in particular, 0-simple and their mutually annihilating unions.

We construct quasi-Hopf algebras associated with a semisimple Lie algebra, a complex curve and a rational differential. This generalizes our previous joint work with V. Rubtsov (Israel J. Math. (1999) and q-alg/9608005).

Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras be a set of nonnegative similarity. Also we find all realizable dimensions two semi-commuting matrices. The last result provides solution problem posed M. Kandi?, K. Šivic (2017) [13].

We present explicit examples finite tensor categories that are C2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras. Mathematics Subject Classification (2010): 18D10, 16W30, 19D23.

We present an alternative constructive proof of the Brauer–Witt theorem using the so-called strongly monomial characters that gives rise to an algorithm for computing the Wedderburn decomposition of semisimple group algebras of finite groups.

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

This section deals with the structure theory of complex semisimple Lie algebras. Some references for this material are [He], [Hu], [J], [K1], [K3], and [V]. Let g be a finite-dimensional Lie algebra. For the moment we shall allow the underlying field to be R or C, but shortly we shall restrict to Lie algebras over C. Semisimple Lie algebras are defined as follows. Let rad g be the sum of all th...

Shiquan Ren Februry, 2010 Abstract: I want to write a summary of my study of complex semisimple Lie algebras, as my thesis for a bachelor degree. The classification of complex semisimple Lie algebras is obtained through the classification of simple root systems. Parallel to it, the classification of compact real Lie algebras can be obtained in a similar way. Only after these two classifications...

For each natural number n, poset T , and |T |–tuple of scalars Q, we introduce the ramified partition algebra P (T) n (Q), which is a physically motivated and natural generalization of the partition algebra [24, 25] (the partition algebra coincides with case |T | = 1). For fixed n and T these algebras, like the partition algebra, have a basis independent of Q. We investigate their representatio...