Given two associative algebras A, C and a linear space V together with some linear maps <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1220_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$R_1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1220_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$R_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1220_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$R_3$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation>, E satisfying some conditions, we define an associative algebra structure on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1220_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">$A\otimes V\otimes C$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mo>⊗</mo> <mi>V</mi> <mo>⊗</mo> <mi>C</mi> </mrow> </math></EquationSource> </InlineEquation> called a two-sided crossed product. Particular cases of this construction are the iterated twisted tensor product of algebras and the two-sided crossed product over a quasi-bialgebra.

Two-sided crossed products

期刊论文
发表日期：

2025年4月22日

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Florin Panaite

摘要

Given two associative algebras A, C and a linear space V together with some linear maps $R_1$ $R_{1}$ , $R_2$ $R_{2}$ , $R_3$ $R_{3}$ , E satisfying some conditions, we define an associative algebra structure on $A\otimes V\otimes C$ $A \otimes V \otimes C$ called a two-sided crossed product. Particular cases of this construction are the iterated twisted tensor product of algebras and the two-sided crossed product over a quasi-bialgebra.