Timeline for Are S(g) and U(g) isomorphic as g-modules for g Lie algebra over F_p ? Are S(g)^g and U(g)^g isomorphic as com.algs ?

8 events

when toggle format	what		by	license	comment
Jun 26, 2012 at 9:40	vote	accept	Alexander Chervov
Jun 25, 2012 at 12:07	comment	added	Alexander Premet		There are similar relations for $\mathfrak{gl}_n$ (any $p$ and any $n$) and for $\frak{sl}_n$ with $p\not\|n$. Sadly, almost nothing is know about the symmetric invariants of $\mathfrak{sl}_{kp}$. Of course, when $p<n$ the invariants $Tr(E^k)$ will fail to generate $S(\mathfrak{gl}_n)^{GL_n}$ (this is because in characteristic $p$ we have that $Tr(E^p)=(Tr(E))^p$). But these can be replaced by the basic invarints arising as the coefficients of the characteristic poynomial of a generic matrix. More on this can be found in my joint paper with Rudolf Tange; see J. Algebra 294 (2005) 177–195.
Jun 25, 2012 at 6:55	comment	added	Alexander Chervov		@Alexander Premet are there relations like formula 1 known for sl_n/ gl_n, not just sl_2 ? I mean in gl_n we have n-Casimirs e.g. Tr(E^k), k=1...n. So we may expect that e_{ij}^p are related to powers of these elements ? May be some nice formulas can be obtained ?
Jun 24, 2012 at 17:32	comment	added	Alexander Chervov		@Alexander Premet Thank you very much !
Jun 24, 2012 at 12:55	history	edited	Alexander Premet	CC BY-SA 3.0	added 166 characters in body
Jun 24, 2012 at 11:57	history	edited	Alexander Premet	CC BY-SA 3.0	added 1 characters in body
Jun 24, 2012 at 11:50	history	edited	Alexander Premet	CC BY-SA 3.0	added 4 characters in body
Jun 24, 2012 at 11:38	history	answered	Alexander Premet	CC BY-SA 3.0