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1.
Hopf group-coalgebras 总被引:2,自引:0,他引:2
Alexis Virelizier 《Journal of Pure and Applied Algebra》2002,171(1):75-122
We study algebraic properties of Hopf group-coalgebras, recently introduced by Turaev. We show the existence of integrals and traces for such coalgebras, and we generalize the main properties of quasitriangular and ribbon Hopf algebras to the setting of Hopf group-coalgebras. 相似文献
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Michael Dokuchaev 《Journal of Pure and Applied Algebra》2007,208(1):77-87
In this article, among other results, we develop a Galois theory of commutative rings under partial actions of finite groups, extending the well-known results by S.U. Chase, D.K. Harrison and A. Rosenberg. 相似文献
3.
Estanislao Herscovich 《Journal of Pure and Applied Algebra》2007,209(1):37-55
We define H-Galois extensions for k-linear categories and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology related to this situation. This spectral sequence is multiplicative and for a group algebra decomposes as a direct sum indexed by conjugacy classes of the group. We also compute some Hochschild-Mitchell cohomology groups of categories with infinite associated quivers. 相似文献
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Lars Kadison 《Journal of Pure and Applied Algebra》2008,212(7):1822-1839
We introduce a notion of depth three tower C⊆B⊆A with depth two ring extension A|B being the case B=C. If and B|C is a Frobenius extension with A|B|C depth three, then A|C is depth two. If A, B and C correspond to a tower G>H>K via group algebras over a base ring F, the depth three condition is the condition that K has normal closure KG contained in H. For a depth three tower of rings, a pre-Galois theory for the ring and coring (A⊗BA)C involving Morita context bimodules and left coideal subrings is applied to specialize a Jacobson-Bourbaki correspondence theorem for augmented rings to depth two extensions with depth three intermediate division rings. 相似文献
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Stefan Ufer 《Journal of Pure and Applied Algebra》2007,210(2):307-320
We consider an interesting class of braidings defined in [S. Ufer, PBW bases for a class of braided Hopf algebras, J. Algebra 280 (2004) 84-119] by a combinatorial property. We show that it consists exactly of those braidings that come from certain Yetter-Drinfeld module structures over pointed Hopf algebras with abelian coradical.As a tool we define a reduced version of the FRT construction. For braidings induced by Uq(g)-modules the reduced FRT construction is calculated explicitly. 相似文献
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A.A. Lopatin 《Linear algebra and its applications》2011,434(8):1920-1944
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,…,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of generic matrices and the traces of tree paths of pairwise different multidegrees, where in the case of characteristic different from two we take only admissible paths. As a consequence, we describe relations modulo decomposable semi-invariants. 相似文献
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Eli Aljadeff 《Advances in Mathematics》2008,218(5):1453-1495
To any cleft Hopf Galois object, i.e., any algebra obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle α, we attach two “universal algebras” and . The algebra is obtained by twisting the multiplication of H with the most general two-cocycle σ formally cohomologous to α. The cocycle σ takes values in the field of rational functions on H. By construction, is a cleft H-Galois extension of a “big” commutative algebra . Any “form” of can be obtained from by a specialization of and vice versa. If the algebra is simple, then is an Azumaya algebra with center . The algebra is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras; it is the universal comodule algebra in which all comodule algebra identities of are satisfied. We construct an embedding of into ; this embedding maps the center of into when the algebra is simple. In this case, under an additional assumption, , thus turning into a central localization of . We completely work out these constructions in the case of the four-dimensional Sweedler algebra. 相似文献
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A general notion of depth two for ring homomorphism N→M is introduced. The step two centralizers A=EndNMN and in the Jones tower above N→M are shown in a natural way via H-equivalence to be dual bimodules for Morita equivalent endomorphism rings, the step one and three centralizers, R=CM(N) and C=EndN-M(M⊗NM). We show A and B to possess dual left and right R-bialgebroid structures which generalize Lu's fundamental bialgebroids over an algebra. There are actions of A and B on M and with Galois properties. If M|N is depth two and Frobenius with R a separable algebra, we show that A and B are dual weak Hopf algebras fitting into a duality-for-actions tower extending previous results in this area for subfactors and Frobenius extensions. 相似文献
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Ignacio L. López Franco 《Journal of Pure and Applied Algebra》2009,213(6):1046-1063
In this article we develop some of the basic constructions of the theory of Hopf algebras in the context of autonomous pseudomonoids in monoidal bicategories. We concentrate on the notion of Hopf modules. We study the existence and the internalisation of this notion, called the Hopf module construction. Our main result is the equivalence between the existence of a left dualization for A (i.e., A is left autonomous) and the validity of an analogue of the structure theorem of Hopf modules. In this case a Hopf module construction for A always exists. We recover from the general theory developed here results on coquasi-Hopf algebras. 相似文献
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Mitja Mastnak 《Journal of Pure and Applied Algebra》2009,213(7):1399-1417
We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf algebras in the recent classification of Andruskiewitsch and Schneider, in an interpretation of these Hopf algebras as graded bialgebra deformations of Radford biproducts. 相似文献
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Sarah Scherotzke 《Journal of Pure and Applied Algebra》2011,215(5):829-838
We construct rank varieties for the Drinfeld double of the Taft algebra Λn and for uq(sl2). For the Drinfeld double when n=2 this uses a result which identifies a family of subalgebras that control projectivity of Λ-modules whenever Λ is a Hopf algebra satisfying a certain homological condition. In this case we show that our rank variety is homeomorphic to the cohomological support variety. We also show that Ext∗(M,M) is finitely generated over the cohomology ring of the Drinfeld double for any finitely generated module M. 相似文献
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We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages induced by diffusion processes on the real line. We give several interpretations and proofs of the main result in terms of noncommutative symmetric and quasi-symmetric functions, as well as generalizations involving matrix quasi-symmetric functions. The interpretation of noncommutative symmetric functions as alien operators in resurgence theory is also discussed, and a new family of Lie idempotents of descent algebras is derived from this interpretation. 相似文献
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By means of a certain module V and its tensor powers in a finite tensor category, we study a question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H is finite. The module V is the counit representation induced from R to H, which is then a generalized permutation module, as well as a module coalgebra. We show that if in the subalgebra pair either Hopf algebra has finite representation type, or V is either semisimple with R∗ pointed, projective, or its tensor powers satisfy a Burnside ring formula over a finite set of Hopf subalgebras including R, then the depth of R in H is finite. One assigns a nonnegative integer depth to V, or any other H-module, by comparing the truncated tensor algebras of V in a finite tensor category and so obtains upper and lower bounds for depth of a Hopf subalgebra. For example, a relative Hopf restricted module has depth 1, and a permutation module of a corefree subgroup has depth less than the number of values of its character. 相似文献
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R. Parthasarathy 《Acta Appl Math》1996,44(1-2):217-256
To a given coherent family of virtual representations of a complex semiesimple Lie algebra we associate elsewhere a coherent family of virtual representations of the corresponding quantum group at roots of unity. We also proposed a conjecture there that under some hyptoheses the members of the family in a certain positive cone are actually modules (and not just a virtual module, i.e., a difference of two modules). The validity of this conjecture for A
2 and B
2 has been verified by the author. In this paper we solve the problem for A
3. 相似文献
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Meson algebras are involved in the wave equation of meson particles in the same way as Clifford algebras are involved in the
Dirac wave equation of electrons. Here we improve and generalize the information already obtained about their structure and
their representations, when the symmetric bilinear form under consideration is nondegenerate. We emphasize their parity grading.
We calculate the center of these meson algebras, and the center of their even subalgebra. Finally we show that every nondegenerate
meson algebra over a field contains a group isomorphic to the group of automorphisms of the symmetric bilinear form.
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