Arithmetic invariants of pseudoreflection groups and regular graded algebras

Rigidity of Graded Regular Algebras

We prove a graded version of Alev-Polo’s rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras An(k) cannot be isomorphic to their fixed subring under any finite group action. We also show the same result for other classes of graded regular algebras including the Sklyanin algebras. 0. Introduction The invarian...

Rings of Generalized and Stable Invariants of Pseudoreflections and Pseudoreflection Groups

ams classification : ams classification : ams classification : 13A50 Invariant Theory summary : summary : summary : Let % : G ! GL(n; IF) be a representation of a nite group G over the eld IF and IFFV ] the space of polynomial functions on V = IF n. We associate to G an

Knit Products of Graded Lie Algebras and Groups

If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a ”double sided semidirect product”. It is called the knit product of the two subalgebras then. The integrated version of this is called a knit product of groups — it coincides with the ZappaSzép product. The behavior of homomorphisms with respect to knit products is invest...

Cartan Invariants of Symmetric Groups and Iwahori-hecke Algebras

Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...

Graded Algebras, Anti-involutions, Simple Groups and Symmetric Spaces