共查询到20条相似文献,搜索用时 19 毫秒
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We classify pointed finite-dimensional complex Hopf algebras whose group of group-like elements is abelian of prime exponent p, p>17. The Hopf algebras we find are members of a general family of pointed Hopf algebras we construct from Dynkin diagrams. As special cases of our construction we obtain all the Frobenius-Lusztig kernels of semisimple Lie algebras and their parabolic subalgebras. An important step in the classification result is to show that all these Hopf algebras are generated by group-like and skew-primitive elements. 相似文献
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单子和余单子的缠绕结构 总被引:6,自引:2,他引:4
研究单子和余单子的缠绕结构和缠绕模以及与代数和余代数的缠绕结构和缠绕模之间的关系,定义了余单子的类群元,得到了一些有意义的结论.最后构造了缠绕模范畴上的两个函子,并证明了它们是伴随函子. 相似文献
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E. G. Puninskii 《Moscow University Mathematics Bulletin》2010,65(5):191-195
V. A. Artamonov and I. A. Chubarov proved a criterion under which an element of some semisimple finite-dimensional Hopf algebra
is group-like. The studied Hopf algebra has only one nonone- dimensional irreducible representation. Let n be a dimension of this representation. It is shown in this paper that for odd prime n the set of group-like elements of these algebras is a cyclic group of order 2n. 相似文献
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HanSong Huang 《中国科学 数学(英文版)》2013,56(4):811-822
Recently, a class of Type II factors has been constructed, arising from holomorphic coverings of bounded planar domains. Those operators in Type II factors act on the Bergman space. In this paper, we develop new techniques to generalize those results to the case of the weighted Bergman spaces. In addition, a class of group-like von Neumann algebras are constructed, which are shown to be *-isomorphic to the group von Neumann algebras. 相似文献
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Sonia Natale 《Algebras and Representation Theory》2004,7(2):173-188
Let p and q be distinct prime numbers. We prove a result on the existence of nontrivial group-like elements in a certain class of semisimple Hopf algebras of dimension pq
r
. We conclude the classification of semisimple Hopf algebras A of dimension pq
2 over an algebraically closed field k of characteristic zero, such that both A and A
* are of Frobenius type. We also complete the classification of semisimple Hopf algebras of dimension pq
2<100. 相似文献
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Yevgenia Kashina 《Algebras and Representation Theory》2016,19(6):1387-1422
In this paper we classify, up to equivalence, all semisimple nontrivial Hopf algebras of dimension 22n+1 for n ≥ 2 over an algebraically closed field of characteristic 0 with the group of group-like elements isomorphic to \(\mathbb {Z}_{2^{n}}\times \mathbb {Z}_{2^{n}}\). Moreover we classify all such nonisomorphic Hopf algebras of dimension 32 and show that they are not twist-equivalent to each other. More generally, given an abelian group of order 2 m?1 we give an upper bound for the number of nonisomorphic nontrivial Hopf algebras of dimension 2 m which have this group as their group of group-like elements. 相似文献
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H.-J. Schneider 《Proceedings of the American Mathematical Society》2001,129(7):1891-1898
A direct proof without modular category theory is given of a recent theorem of Etingof and Gelaki (1998) on the dimensions of irreducible representations. Factorizable Hopf algebras are characterized in terms of their Drinfeld double, and their character rings and the group-like elements of their duals are described.
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This is a contribution to the classification of finite-dimensional pointed Hopf algebras. We are concerned with the case when the group of group-like elements is Abelian of exponent 2. We attach to such a pointed Hopf algebra a generalized simply-laced Cartan matrix; we conjecture that the Hopf algebra is finite-dimensional if and only if the Cartan matrix is of finite type. We prove the conjecture for the types An and An(1). We obtain the classification of all possible Hopf algebras with Cartan matrix An. We use the lifting method developed by Hans-Jürgen Schneider and the first-named author.
Presented by S. MontgomeryMathematics Subject Classifications (2000) Primary: 17B37; secondary: 16W30.This work was partially supported by CONICET, Agencia Córdoba Ciencia – CONICOR, FOMEC and Secyt (UNC). 相似文献
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In this paper, we prove the Donoho–Stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi-shifts of group-like projections. We also prove the Hirschman–Beckner uncertainty principle for compact quantum groups and discrete quantum groups. Furthermore, we show Hardy's uncertainty principle for locally compact quantum groups in terms of bi-shifts of group-like projections. 相似文献
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Rodríguez-Nieto José Gregorio Salazar-Díaz Olga P. Velásquez Raúl 《Semigroup Forum》2021,102(3):861-884
Semigroup Forum - In this paper we extend some group-like concepts to generalized digroups. We exhibit examples of non-abelian cyclic generalized digroups. We show that abelian generalized digroups... 相似文献
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Camille Laurent-Gengoux Abdenacer Makhlouf Joana Teles 《Journal of Pure and Applied Algebra》2018,222(5):1139-1163
We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra. 相似文献
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Akihide Hanaki 《Journal of Combinatorial Theory, Series A》2008,115(2):226-236
We give a definition of nilpotent association schemes as a generalization of nilpotent groups and investigate their basic properties. Moreover, for a group-like scheme, we characterize the nilpotency by its character products. 相似文献
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Ettore Aldrovandi 《Journal of Pure and Applied Algebra》2008,212(5):994-1038
We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification result in terms of hypercohomology groups with values in abelian crossed squares and cones of morphisms of complexes of length 3. We give an application to the geometric construction of certain elements in Hermitian Deligne cohomology groups. 相似文献
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We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the action is scalar. This generalizes an analogous result for group actions by automorphisms obtained by Dicks and Formanek, and Kharchenko. 相似文献
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《Discrete Mathematics》2022,345(6):112822
We consider a generalization of the Brauer-Wielandt-Harada Theorem to group-like regular association schemes. As an application, we give a necessary condition for commutative association schemes to be regular. Moreover, we derive the number of irreducible characters of multiplicity 1 from the product of all adjacency matrices and all valencies for a commutative regular association scheme. 相似文献
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Tracy L. Payne 《Annals of Global Analysis and Geometry》2012,41(2):139-160
We present new tools for determining whether two nilpotent metric Lie algebras are in the same isometry class. We exhibit
new examples of continuous families of nilsoliton metric Lie algebras, including deformations of uniform metric Lie algebras.
We show that all algebras of generalized Heisenberg type except for Heisenberg algebras and two others admit deformations
by nilsoliton metric Lie algebras. 相似文献
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Lakhdar Hammoudi 《Results in Mathematics》1996,29(3-4):227-232
We investigate homomorphic images of Golod algebras. We prove that some quotients of certain Golod algebras are Golod algebras too. We determine classes of Golod algebras and nilalgebras not satisfying Golod properties which have a continuum of non isomorphic homomorphic images. We establish analogous results for Lie algebras and p-groups of Golod type. 相似文献