On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component

Thomas B. Gregory; Michael I. Kuznetsov

On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component

Rings and Algebras 2018-06-28 v3

Authors: Thomas B. Gregory , Michael I. Kuznetsov

Abstract

We consider finite-dimensional irreducible transitive graded Lie algebras $L = \sum_{i=-q}^rL_i$ over algebraically closed fields of characteristic three. We assume that the null component $L_0$ is classical and reductive. The adjoint representation of $L$ on itself induces a representation of the commutator subalgebra $L_0'$ of the null component on the minus-one component $L_{-1}.$ We show that if the depth $q$ of $L$ is greater than one, then this representation must be restricted.

Keywords

graded Lie algebras characteristic three classical reductive null component adjoint representation restricted representation depth

Cite

@article{arxiv.1706.00534,
  title  = {On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component},
  author = {Thomas B. Gregory and Michael I. Kuznetsov},
  journal= {arXiv preprint arXiv:1706.00534},
  year   = {2018}
}

Comments

46 pages; correct typos; change argument; one hypothesis of result changed: height of Lie algebra now required to be at least two

On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component

Abstract

Keywords

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