University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > First cohomology of Frobenius kernels and truncated invariants

First cohomology of Frobenius kernels and truncated invariants

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k be an algebraically closed field of characteristic p > 0 and let G be a connected reductive group over k with Lie algebra g. Consider the rings k[G] and k[g] of regular functions on G and g as G-modules via the conjugation action. They have been studied extensively, for example in Kostant’s 1963 paper.

I will discuss the result that, under some mild assumptions, the first restricted cohomology of these modules is zero.

After this I will discuss the problem of describing the invariants in a certain finite dimensional quotient of k[gl_n]. This is related to the centre of the restricted enveloping algebra of gl_n.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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