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...

We prove that if L = lim ←−Ln (n ∈ N), where each Ln is a finite dimensional semisimple Lie algebra, and A is a finite codimensional ideal of L, then L/A is also semisimple. We show also that every finite dimensional homomorphic image of the cartesian product of solvable (nilpotent) finite dimensional Lie algebras is solvable (nilpotent). Mathematics Subject Classification: 14L, 16W, 17B45

In this paper, we give a necessary and sufficient condition for a Brauer algebra to be semisimple.

In one of his last papers, Boris Weisfeiler proved that if modular semisimple Lie algebra possesses a solvable maximal subalgebra which defines in it a long filtration, then associated graded algebra is isomorphic to one constructed from the Zassenhaus algebra tensored with the divided powers algebra. We completely determine such class of algebras, calculating in process low-dimensional cohomol...

We define a nontrivial homomorphism from the Hecke algebra of type B onto a reduced algebra of the Hecke algebra of type A at roots of unity. We use this homomorphism to describe semisimple quotients of the Hecke algebra of type B at roots of unity. Using these quotients we determine subfactors obtained from the inclusion of Hecke algebra of type A into Hecke algebras of type B. We also study i...

We decompose tensor products of the defining representation of a Cartan type Lie algebra W (n) in the case where the number of tensoring does not exceed the rank of the Lie algebra. As a result, we get a kind of Schur duality between W (n) and a finite dimensional non-semisimple algebra, which is the semi-group ring of the transformation semigroup Tm .

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping algebra by a suitable ideal.

States of unital Abelian lattice-groups (normalised positive group homomorphisms to R) provide an abstraction expected-value operators. A well-known theorem due Mundici asserts that the category (with unit-preserving lattice-group as morphisms) is equivalent algebraic MV-algebras, and their homomorphisms. Through this equivalence, states correspond certain [0,1]-valued functionals on which are ...

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...

We study forms of coalgebras and Hopf algebras (i.e. coalgebras and Hopf algebras which are isomorphic after a suitable extension of the base field). We classify all forms of grouplike coalgebras according to the structure of their simple subcoalgebras. For Hopf algebras, given a W ∗-Galois field extension K ⊆ L for W a finite-dimensional semisimple Hopf algebra and a K-Hopf algebra H, we show ...