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- W4301040450 abstract "Let q be a simple algebraic group of type A or C over a field of good positive characteristic. We show for any x in q =Lie(Q) that the invariant algebra S(q_x)^{q_x} is generated by the p^{th} power subalgebra and the mod p reduction of the characteristic zero invariant algebra. The latter algebra is known to be polynomial cite{PPY} and we show that it remains so after reduction. Using a theory of symmetrisation in positive characteristic we prove the analogue of this result in the enveloping algebra, where the p-centre plays the role of the p^{th} power subalgebra. In Zassenhaus' foundational work cite{Zas}, the invariant theory and representation theory of modular Lie algebras were shown to be explicitly intertwined. We exploit his theory to give a precise upper bound for the dimensions of simple q_x-modules. When g is of type A and g = k oplus p is a symmetric decomposition of orthogonal type we use similar methods to show that for every nilpotent e in k the invariant algebra S(p_e)^{k_e} is generated by the p^{th} power subalgebra and S(p_e)^{K_e} which is also shown to be polynomial." @default.
- W4301040450 created "2022-10-04" @default.
- W4301040450 creator A5004049646 @default.
- W4301040450 date "2011-08-10" @default.
- W4301040450 modified "2023-10-16" @default.
- W4301040450 title "Invariants of Centralisers in Positive Characteristic" @default.
- W4301040450 doi "https://doi.org/10.48550/arxiv.1108.2306" @default.
- W4301040450 hasPublicationYear "2011" @default.
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