Conical polynomials are defined as certain polynomials in quadratic elements of the universal enveloping algebra of a semisimple symmetric Lie algebra over a field of characteristic zero. These polynomials were used in an earlier paper to describe the conical vectors in certain induced modules. Here it is shown that when the base field is extended to a certain type of nonassociative algebra, th...

In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that...

The Weil algebra of a semisimple Lie group and an exterior algebra of a symplectic manifold possess antibrackets. They are applied to formulate the models of non{abelian equivariant cohomologies. e-mail: [email protected]

The Weil algebra of a semisimple Lie group and an exterior algebra of a sym-plectic manifold possess antibrackets. They are applied to formulate the models of non–abelian equivariant cohomologies.

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of simple modules subcharacter algebra finite group. abelian groups, prove deformation given by inclusion natural numbers, which corresponds to generated fibred bisets over field characteristic zero, is not semisimple. In cyclic group prime order case, provide complete description semisimple deform...

In this paper we show that the K-algebra (G, ·, , e) on an abelian group (G, ·) is equivalent to the p-semisimple BCI-algebra (G; , e). Mathematics Subject Classification: 06F35, 20A05.