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arXiv · 0712.2551

Artin-Schelter Regular Algebras, Subalgebras, and Pushouts

Jun Zhang
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Abstract

Take $A$ to be a regular quadratic algebra of global dimension three. We observe that there are examples of $A$ containing a dimension three regular cubic algebra $C$. If $B$ is another dimension three regular quadratic algebra, also containing $C$ as a subalgebra, then we can form the pushout algebra $D$ of the inclusions $i_1:C\hookrightarrow A$ and $i_2:C\hookrightarrow B$. We show that for a certain class of regular algebras $C\hookrightarrow A,B$, their pushouts $D$ are regular quadratic algebras of global dimension four. Furthermore, some of the point module structures of the dimension three algebras get passed on to the pushout algebra $D$.

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Jun Zhang. 2010-09-02. Artin-Schelter Regular Algebras, Subalgebras, and Pushouts. https://arxiv.org/abs/0712.2551

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