On ID*-superderivations of Lie superalgebras

Abstract

Let L be a Lie superalgebra over a field of characteristic different from 2, 3 and write ${\mathrm{I}\mathrm{D}}^{\ast }\left(L\right)$ for the Lie superalgebra consisting of superderivations mapping L to $L^2$ and the central elements to zero. In this paper we first give an upper bound for the superdimension of ${\mathrm{I}\mathrm{D}}^{\ast }\left(L\right)$ by means of linear vector space decompositions. Then we characterize the ${\mathrm{I}\mathrm{D}}^{\ast }$-superderivation superalgebras for the nilpotent Lie superalgebras of class 2 and the model filiform Lie superalgebras by methods of block matrices.

Keywords:

• ${\mathrm{I}\mathrm{D}}^{\ast }$-superderivation
• nilpotent Lie superalgebras of class 2
• model filiform Lie superalgebras

Mathematics Subject Classification 2010:

• 17B05
• 17B30
• 17B56

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by National Natural Science Foundation of China [grants numbers 11471090, 11701158].