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- W2084552199 abstract "Verbally prime algebras are important in PI theory. They are well known over a field $K$ of characteristic zero: 0 and $K<T>$ (the trivial ones), $M_n(K)$, $M_n(E)$, $M_{ab}(E)$. Here $K<T>$ is the free associative algebra with free generators $T$, $E$ is the infinite dimensional Grassmann algebra over $K$, $M_n(K)$ and $M_n(E)$ are the $ntimes n$ matrices over $K$ and over $E$, respectively. Moreover $M_{ab}(E)$ are certain subalgebras of $M_{a+b}(E)$, defined below. The generic algebras of these algebras have been studied extensively. Procesi gave a very tight description of the generic algebra of $M_n(K)$. The situation is rather unclear for the remaining nontrivial verbally prime algebras. In this paper we study the centre of the generic algebra of $M_{11}(E)$ in two generators. We prove that this centre is a direct sum of the field and a nilpotent ideal (of the generic algebra). We describe the centre of this algebra. As a corollary we obtain that this centre contains nonscalar elements thus we answer a question posed by Berele." @default.
- W2084552199 created "2016-06-24" @default.
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- W2084552199 date "2013-02-01" @default.
- W2084552199 modified "2023-09-30" @default.
- W2084552199 title "The centre of generic algebras of small PI algebras" @default.
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- W2084552199 doi "https://doi.org/10.1016/j.jalgebra.2012.11.018" @default.
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