Restricted shifted Yangians and restricted finite ????-algebras

Twisted Yangians and finite W-algebras

We construct an explicit set of generators for the finite W -algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such finite W -algebras are quotients of twisted Yangians.

On Restricted Leibniz Algebras

In this paper we prove that in prime characteristic there is a functor −p-Leib from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras. Moreover we define the notion of restricted universal enveloping diassociative algebra Udp(g) of a restricted Leibniz algebra g and we show that Ud...

Restricted Lie Algebras

Shapovalov Determinant for Restricted and Quantized Restricted Enveloping Algebras

As is well known, the Shapovalov bilinear form and its determinant is an important tool in the representation theory of semisimple Lie algebras over char. 0. To our knowledge, the corresponding study of the Shapovalov bilinear form and its determinant is not available in the literature in char. p or the quantum case at roots of unity. The aim of this paper is to fully determine the Shapovalov d...

The Restricted Isomorphism Problem for Metacyclic Restricted Lie Algebras

Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...