The classification theorem for semisimple Lie algebras states that up to isomorphy any finite dimensional semisimple Lie algebra g defined over an algebraically closed field is uniquely determined by the root system of a maximal toral subalgebra. Moreover, if g is simple, then this root system is irreducible and its Dynkin diagram must be one of An, Bn, Cn, Dn, E6, E7, E8, F4, or G2. This is fu...

Abstract For a semisimple Lie algebra defined over discrete valuation ring with field of fractions K , we prove that any primitive ideal rational central character in the affinoid enveloping algebra, $$\widehat{U({\mathfrak {g}})_{K}}$$ U ( g )</...

In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module...

A new class of abelian p-groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).

A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.

We study disemisimple Lie algebras, i.e., algebras which can be written as a vector space sum of two semisimple subalgebras. show that algebra g is if and only its solvable radical coincides with nilradical prehomogeneous s-module for Levi subalgebra s g. use the classification s-modules simple given by Vinberg to abelian. extend this result having no quotients type A.

The main purpose of the present paper is to lay foundations generalizing AdS/CFT (holography) idea beyond conformal setting. tool find suitable realizations bulk and boundary via group theory. We use all ten families classical real semisimple Lie groups $G$ algebras $\cal G$. For this are used several algebra decompositions: global Iwasawa decomposition local Bruhat Sekiguchi-like decomposititi...

We present an algorithm to compute the Wedderburn decomposition of semisimple group algebras based on a computational approach of the Brauer-Witt theorem. The algorithm was implemented in the GAP package wedderga.