Author: D. Bulacu
Publisher: American Mathematical Soc.
ISBN: 1470447525
Category : Education
Languages : en
Pages : 133
Book Description
We introduce (pre-)Galois and cleft monoidal cowreaths. Generalizing a result of Schneider, to any pre-Galois cowreath we associate a pair of adjoint functors L R and give necessary and sufficient conditions for the adjunction to be an equivalence of categories. Inspired by the work of Doi we also give sufficient conditions for L R to be an equivalence, and consequently conditions under which a fundamental structure theorem for entwined modules over monoidal cowreaths holds. We show that a cowreath is cleft if and only if it is Galois and has the normal basis property; this generalizes a result concerning Hopf cleft extensions due to Doi and Takeuchi. Furthermore, we show that the cleft cowreaths are in a one to one correspondence with what we call cleft wreaths. The latter are wreaths in the sense of Lack and Street, equipped with two additional morphisms satisfying some compatibility relations. Note that, in general, the algebras defined by cleft wreaths cannot be identified to (generalized) crossed product algebras, as they were defined by Doi and Takeuchi, and Blattner, Cohen and Montgomery. This becomes more transparent when we apply our theory to cowreaths defined by actions and coactions of a quasi-Hopf algebra, monoidal entwining structures and ν-Doi-Hopf structures, respectively. In particular, we obtain that some constructions of Brzezi´nski and Schauenburg produce examples of cleft wreaths, and therefore of cleft cowreaths, too.
Galois and Cleft Monoidal Cowreaths. Applications
Author: D. Bulacu
Publisher: American Mathematical Soc.
ISBN: 1470447525
Category : Education
Languages : en
Pages : 133
Book Description
We introduce (pre-)Galois and cleft monoidal cowreaths. Generalizing a result of Schneider, to any pre-Galois cowreath we associate a pair of adjoint functors L R and give necessary and sufficient conditions for the adjunction to be an equivalence of categories. Inspired by the work of Doi we also give sufficient conditions for L R to be an equivalence, and consequently conditions under which a fundamental structure theorem for entwined modules over monoidal cowreaths holds. We show that a cowreath is cleft if and only if it is Galois and has the normal basis property; this generalizes a result concerning Hopf cleft extensions due to Doi and Takeuchi. Furthermore, we show that the cleft cowreaths are in a one to one correspondence with what we call cleft wreaths. The latter are wreaths in the sense of Lack and Street, equipped with two additional morphisms satisfying some compatibility relations. Note that, in general, the algebras defined by cleft wreaths cannot be identified to (generalized) crossed product algebras, as they were defined by Doi and Takeuchi, and Blattner, Cohen and Montgomery. This becomes more transparent when we apply our theory to cowreaths defined by actions and coactions of a quasi-Hopf algebra, monoidal entwining structures and ν-Doi-Hopf structures, respectively. In particular, we obtain that some constructions of Brzezi´nski and Schauenburg produce examples of cleft wreaths, and therefore of cleft cowreaths, too.
Publisher: American Mathematical Soc.
ISBN: 1470447525
Category : Education
Languages : en
Pages : 133
Book Description
We introduce (pre-)Galois and cleft monoidal cowreaths. Generalizing a result of Schneider, to any pre-Galois cowreath we associate a pair of adjoint functors L R and give necessary and sufficient conditions for the adjunction to be an equivalence of categories. Inspired by the work of Doi we also give sufficient conditions for L R to be an equivalence, and consequently conditions under which a fundamental structure theorem for entwined modules over monoidal cowreaths holds. We show that a cowreath is cleft if and only if it is Galois and has the normal basis property; this generalizes a result concerning Hopf cleft extensions due to Doi and Takeuchi. Furthermore, we show that the cleft cowreaths are in a one to one correspondence with what we call cleft wreaths. The latter are wreaths in the sense of Lack and Street, equipped with two additional morphisms satisfying some compatibility relations. Note that, in general, the algebras defined by cleft wreaths cannot be identified to (generalized) crossed product algebras, as they were defined by Doi and Takeuchi, and Blattner, Cohen and Montgomery. This becomes more transparent when we apply our theory to cowreaths defined by actions and coactions of a quasi-Hopf algebra, monoidal entwining structures and ν-Doi-Hopf structures, respectively. In particular, we obtain that some constructions of Brzezi´nski and Schauenburg produce examples of cleft wreaths, and therefore of cleft cowreaths, too.
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
Author: Stefan Geiss
Publisher: American Mathematical Society
ISBN: 1470449358
Category : Mathematics
Languages : en
Pages : 112
Book Description
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Publisher: American Mathematical Society
ISBN: 1470449358
Category : Mathematics
Languages : en
Pages : 112
Book Description
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
Author: William Gignac
Publisher: American Mathematical Society
ISBN: 1470449587
Category : Mathematics
Languages : en
Pages : 100
Book Description
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Publisher: American Mathematical Society
ISBN: 1470449587
Category : Mathematics
Languages : en
Pages : 100
Book Description
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Goodwillie Approximations to Higher Categories
Author: Gijs Heuts
Publisher: American Mathematical Society
ISBN: 1470448939
Category : Mathematics
Languages : en
Pages : 108
Book Description
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Publisher: American Mathematical Society
ISBN: 1470448939
Category : Mathematics
Languages : en
Pages : 108
Book Description
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Non-Kissing Complexes and Tau-Tilting for Gentle Algebras
Author: Yann Palu
Publisher: American Mathematical Society
ISBN: 1470450046
Category : Mathematics
Languages : en
Pages : 95
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450046
Category : Mathematics
Languages : en
Pages : 95
Book Description
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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups
Author: Pierre Patie
Publisher: American Mathematical Society
ISBN: 1470449366
Category : Mathematics
Languages : en
Pages : 182
Book Description
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Publisher: American Mathematical Society
ISBN: 1470449366
Category : Mathematics
Languages : en
Pages : 182
Book Description
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On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
Author: Athanassios S. Fokas
Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114
Book Description
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Intense Automorphisms of Finite Groups
Author: Mima Stanojkovski
Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117
Book Description
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Elliptic Theory for Sets with Higher Co-Dimensional Boundaries
Author: Guy David
Publisher: American Mathematical Society
ISBN: 1470450437
Category : Mathematics
Languages : en
Pages : 123
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450437
Category : Mathematics
Languages : en
Pages : 123
Book Description
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The Yang-Mills Heat Equation with Finite Action in Three Dimensions
Author: Leonard Gross
Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111
Book Description
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Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111
Book Description
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