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arXiv · 2006.14541

Relatively free algebras of finite rank

Thiago Castilho de Mello·Felipe Yukihide Yasumura
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Abstract

Let $\mathbb{K}$ be a field of characteristic zero and $B=B_0+B_1$ a finite dimensional associative superalgebra. In this paper we investigate the polynomial identities of the relatively free algebras of finite rank of the variety $\mathfrak V$ defined by the Grassmann envelope of $B$. We also consider the $k$-th Grassmann Envelope of $B$, $G^{(k)}(B)$, constructed with the $k$-generated Grassmann algebra, instead of the infinite dimensional Grassmann algebra. We specialize our studies for the algebra $UT_2(G)$ and $UT_2(G^{(k)})$, which can be seen as the Grassmann envelope and $k$-th Grassmann envelope, respectively, of the superalgebra $UT_2(\mathbb{K}[u])$, where $u^2=1$.

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Thiago Castilho de Mello, Felipe Yukihide Yasumura. 2020-06-25. Relatively free algebras of finite rank. https://doi.org/10.1007/978-3-030-63111-6_8

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