Segre products and Segre morphisms in a class of Yang–Baxter algebras

被引：0

作者：

Tatiana Gateva-Ivanova

机构：

[1] Max Planck Institute for Mathematics,

[2] American University in Bulgaria,undefined

来源：

Letters in Mathematical Physics | / 113卷

关键词：

Quadratic algebras; PBW algebras; Koszul algebras; Segre products; Segre maps; Yang–Baxter equation; Yang–Baxter algebras; Primary 16S37; 16T25; 16S38; 16S15; 81R60;

D O I：

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中图分类号：

学科分类号：

摘要：

Let (X,rX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X,r_X)$$\end{document} and (Y,rY)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Y,r_Y)$$\end{document} be finite nondegenerate involutive set-theoretic solutions of the Yang–Baxter equation, and let AX=A(k,X,rX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_X = \mathcal {A}({{\textbf {k}}}, X, r_X)$$\end{document} and AY=A(k,Y,rY)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_Y= \mathcal {A}({{\textbf {k}}}, Y, r_Y)$$\end{document} be their quadratic Yang–Baxter algebras over a field k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\textbf {k}}}$$\end{document}. We find an explicit presentation of the Segre product AX∘AY\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_X\circ A_Y$$\end{document} in terms of one-generators and quadratic relations. We introduce analogues of Segre maps in the class of Yang–Baxter algebras and find their images and their kernels. The results agree with their classical analogues in the commutative case.

引用

共 24 条

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