On simple Filippov superalgebras of type A(m,n)
Patr\'icia Damas Beites, Alexander Petrovich Pozhidaev
TL;DR
This paper proves the non-existence of simple finite-dimensional Filippov superalgebras of type A(m,n) over algebraically closed fields of characteristic zero.
Contribution
It establishes a non-existence theorem for simple finite-dimensional Filippov superalgebras of a specific type, filling a gap in algebraic superalgebra classification.
Findings
No simple finite-dimensional Filippov superalgebras of type A(m,n) exist over algebraically closed fields of characteristic zero.
The proof relies on structural properties of superalgebras.
This result narrows the classification of Filippov superalgebras.
Abstract
It is proved that there exist no simple finite-dimensional Filippov superalgebras of type A(m,n) over an algebraically closed field of characteristic 0.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic structures and combinatorial models