Symmetrical invariants of some modular Lie algebras of Cartan type

Details Symmetrical invariants of some modular Lie algebras of Cartan type Symmetrical invariants of some modular Lie algebras of Cartan type

2007-04-24

arxiv.org/abs/0704.3254v1

Mat. Stud. 30, No. 1, 3-8 (2008).

Mathematics

Rings and Algebras

7 pages in Ukrainian

Scientific paper

Let $L$ be one of the finite dimensional Lie algebras $W_n({\bf m}),$ $S_n({\bf m}),$ $ H_n({\bf m})$ of Cartan type over an algebraically closed field of prime characteristic $p>0.$ For an elements $F$ of the symmetrical algebra $S(L)$ we found necessary and sufficient condition in order to the element $ad(\partial_1)^{p^{m_1}-1} ad(\partial_2)^{p^{m_2}-1}... ad(\partial_n)^{p^{m_n}-1}(F)$ belongs to the symmetrical invariants algebra $S(L)^L.$ Also, for $p=3,5$ the algebra of symmetrical invariants $S(H_2)^{H_2}$ is calculated in explicit way.

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