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- W2010612963 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>be a weak crossed Hopf group coalgebra over group<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>Ο</mml:mi></mml:mrow></mml:math>; we first introduce a kind of new Ξ± -Yetter-Drinfelβd module categories<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>π²</mml:mi><mml:mi>π΄</mml:mi><mml:msub><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant=normal>Ξ±</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>Ξ±</mml:mi><mml:mo>β</mml:mo><mml:mi>Ο</mml:mi></mml:math>and use it to construct a braided<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math>-category<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>π²</mml:mi><mml:mi>π΄</mml:mi><mml:mi>π</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>. As an application, we give the concept of a Long dimodule category<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:msub><mml:mrow><mml:mi mathvariant=normal /></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msub><mml:mi>π²</mml:mi><mml:msup><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msup></mml:math>for a weak crossed Hopf group coalgebra<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>with quasitriangular and coquasitriangular structures and obtain that<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:msub><mml:mrow><mml:mi mathvariant=normal /></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msub><mml:mi>π²</mml:mi><mml:msup><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msup></mml:math>is a braided<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math>-category by translating it into a weak Yetter-Drinfel'd module subcategory<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mi>π²</mml:mi><mml:mi>π΄</mml:mi><mml:mi>π</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>H</mml:mi><mml:mo>β</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>." @default.
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- W2010612963 date "2013-01-01" @default.
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- W2010612963 title "New BraidedT-Categories over Weak Crossed Hopf Group Coalgebras" @default.
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- W2010612963 doi "https://doi.org/10.1155/2013/626394" @default.
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