Let F be an algebraically closed field of characteristic zero and let (A_1, ..., A_n) be an n-tuple of simple superalgebras such that n ≥ 3 and there exists 1 < r < n such that , A_r = M_k(F+cF) with c^2 = 1, whereas A-i = M_{k_i , l_i} (F) for all remaining indices. In this paper, we classify the minimal F-superalgebras such that its graded semisimple part is given by A_1 + ....+ A_n Moreover, we obtain necessary and sufficient conditions to the supervariety generated by such minimal superalgebra be or not minimal of superexponent dim (A_1 + ....+ A_n).
On the classification of a family of minimal superalgebras
Di Vincenzo O. M.;
2020-01-01
Abstract
Let F be an algebraically closed field of characteristic zero and let (A_1, ..., A_n) be an n-tuple of simple superalgebras such that n ≥ 3 and there exists 1 < r < n such that , A_r = M_k(F+cF) with c^2 = 1, whereas A-i = M_{k_i , l_i} (F) for all remaining indices. In this paper, we classify the minimal F-superalgebras such that its graded semisimple part is given by A_1 + ....+ A_n Moreover, we obtain necessary and sufficient conditions to the supervariety generated by such minimal superalgebra be or not minimal of superexponent dim (A_1 + ....+ A_n).File in questo prodotto:
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