Galois and Cleft Monoidal Cowreaths. Applications

Galois and Cleft Monoidal Cowreaths. Applications PDF Author: D. Bulacu
Publisher: American Mathematical Soc.
ISBN: 1470447525
Category : Education
Languages : en
Pages : 133

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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

Galois and Cleft Monoidal Cowreaths. Applications PDF Author: D. Bulacu
Publisher: American Mathematical Soc.
ISBN: 1470447525
Category : Education
Languages : en
Pages : 133

Get Book Here

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

Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs PDF Author: Stefan Geiss
Publisher: American Mathematical Society
ISBN: 1470449358
Category : Mathematics
Languages : en
Pages : 112

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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities

Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities PDF Author: William Gignac
Publisher: American Mathematical Society
ISBN: 1470449587
Category : Mathematics
Languages : en
Pages : 100

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Goodwillie Approximations to Higher Categories

Goodwillie Approximations to Higher Categories PDF Author: Gijs Heuts
Publisher: American Mathematical Society
ISBN: 1470448939
Category : Mathematics
Languages : en
Pages : 108

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Non-Kissing Complexes and Tau-Tilting for Gentle Algebras

Non-Kissing Complexes and Tau-Tilting for Gentle Algebras PDF Author: Yann Palu
Publisher: American Mathematical Society
ISBN: 1470450046
Category : Mathematics
Languages : en
Pages : 95

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Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups

Spectral Expansions of Non-Self-Adjoint Generalized Laguerre Semigroups PDF Author: Pierre Patie
Publisher: American Mathematical Society
ISBN: 1470449366
Category : Mathematics
Languages : en
Pages : 182

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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

On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function PDF Author: Athanassios S. Fokas
Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114

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Intense Automorphisms of Finite Groups

Intense Automorphisms of Finite Groups PDF Author: Mima Stanojkovski
Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117

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Elliptic Theory for Sets with Higher Co-Dimensional Boundaries

Elliptic Theory for Sets with Higher Co-Dimensional Boundaries PDF Author: Guy David
Publisher: American Mathematical Society
ISBN: 1470450437
Category : Mathematics
Languages : en
Pages : 123

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The Yang-Mills Heat Equation with Finite Action in Three Dimensions

The Yang-Mills Heat Equation with Finite Action in Three Dimensions PDF Author: Leonard Gross
Publisher: American Mathematical Society
ISBN: 1470450534
Category : Mathematics
Languages : en
Pages : 111

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