共查询到20条相似文献,搜索用时 0 毫秒
1.
George E. Andrews Li Guo William Keigher Ken Ono 《Transactions of the American Mathematical Society》2003,355(11):4639-4656
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
2.
For G a finite abelian group, we study the properties of general equivalence relations on G
n
= G
n
⋊
n
, the wreath product of G with the symmetric group
n
, also known as the G-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of
G
n
as well as graded connected Hopf subalgebras of ⨁
n≥ o
G
n
. In particular we construct a G-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or G-coloured descent algebra). We show that the direct sum of the G-coloured peak algebras is a Hopf algebra. We also have similar results for a G-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the G-coloured descent Hopf algebra whose image is the G-coloured peak Hopf algebra. We outline a theory of combinatorial G-coloured Hopf algebra for which the G-coloured quasi-symmetric Hopf algebra and the graded dual to the G-coloured peak Hopf algebra are central objects.
2000 Mathematics Subject Classification Primary: 16S99; Secondary: 05E05, 05E10, 16S34, 16W30, 20B30, 20E22Bergeron is partially supported by NSERC and CRC, CanadaHohlweg is partially supported by CRC 相似文献
3.
G. C. Wraith 《Annali di Matematica Pura ed Applicata》1967,76(1):149-163
Summary In any category with products and a terminal object one may define the notions of group, module over a group etc. if f: R′→R
is a homomorphism of groups, and M an R-module, then one has an induced R′-module f*(M). If one is working in the category
of sets, one may define a functor left adjoint to f* by N→R⊗R′ N, where N is an R′-module. In this paper we show that f* has a left adjoint when one is working in the category of graded
connected coalgebras over a field. 相似文献
4.
In this work we construct an example of a generalized Jacobian of an elliptic curve defined over a field of algebraic numbers k such that the Serre Lie algebra p-adic representation of the Galois group of the algebraic closure of the field k in its Tate module is irreducible.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 571–576, April, 1976.In conclusion the authors thank O. N. Vvedenskii for guidance in this work. 相似文献
5.
6.
Quiver Hopf algebras 总被引:1,自引:0,他引:1
In this paper we study subHopfalgebras of graded Hopf algebra structures on a path coalgebra kQc. We prove that a Hopf structure on some subHopfquivers can be lifted to a Hopf structure on the whole Hopf quiver. If Q is a Schurian Hopf quiver, then we classified all simple-pointed subHopfalgebras of a graded Hopf structure on kQc. We also prove a dual Gabriel theorem for pointed Hopf algebras. 相似文献
7.
8.
9.
R. B. Mukhatov 《Mathematical Notes》2013,93(1-2):143-150
In the paper, for semisimple Hopf algebras that have only one non-one-dimensional irreducible representation, all Hopf ideals are described and, under some restriction concerning the number of group elements in the dual Hopf algebra, some series of Hopf subalgebras are found. Moreover, the quotient Hopf algebras of these semisimpleHopf algebras are described. 相似文献
10.
D. Stefan 《Proceedings of the American Mathematical Society》1997,125(11):3191-3193
In this paper we construct certain Hopf subalgebras of a pointed Hopf algebra over a field of characteristic 0. Some applications are given in the case of Hopf algebras of dimension 6, and , where and are different prime numbers.
11.
《Journal of Pure and Applied Algebra》1987,47(3):243-252
An algebraic theory of bordism via characteristic numbers, analogous to topological bordism, is given. The Steenrod algebra is replaced by a fairly general graded Hopf algebra A, topological spaces by algebras over A, vector bundles by Thom modules, and closed manifolds by Poincaré algebras over A. 相似文献
12.
Zhi-xiang Wu 《高校应用数学学报(英文版)》2018,33(1):107-126
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized. 相似文献
13.
L. Foissy 《Journal of Pure and Applied Algebra》2012,216(2):480-494
We first prove that a graded, connected, free and cofree Hopf algebra is always self-dual. Then, we prove that two graded, connected, free and cofree Hopf algebras are isomorphic if and only if they have the same Poincaré–Hilbert formal series. If the characteristic of the base field is zero, we prove that the Lie algebra of the primitive elements of such an object is free, and we deduce a characterization of the formal series of free and cofree Hopf algebras by a condition of growth of the coefficients. We finally show that two graded, connected, free and cofree Hopf algebras are isomorphic as (nongraded) Hopf algebras if and only if the Lie algebras of their primitive elements have the same number of generators. 相似文献
14.
The concept of (f, σ)-pair (B, H)is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an (f, σ)-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel'd category H^HYD by twisting the multiplication of B. 相似文献
15.
In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra. We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E. L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite- dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual. 相似文献
16.
17.
Florent Hivert Jean-Christophe Novelli Jean-Yves Thibon 《Journal of Algebraic Combinatorics》2008,28(1):65-95
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures and
investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based
on graphs, and its noncommutative dual is realized in three different ways, in particular, as the Grossman–Larson algebra
of heap-ordered trees. Extensions to endofunctions, parking functions, set compositions, set partitions, planar binary trees,
and rooted forests are discussed. Finally, we introduce one-parameter families interpolating between different structures
constructed on the same combinatorial objects. 相似文献
18.
R. B. Mukhatov 《Moscow University Mathematics Bulletin》2011,66(1):44-46
The paper considers a classification of semisimple Hopf algebras having exactly one irreducible non-one-dimensional representation
under a certain condition on the number of group elements. 相似文献
19.
Jiangwei Xue 《Journal of Number Theory》2011,131(2):332-342
Text
Let p be a prime, and q a power of p. Using Galois theory, we show that over a field K of characteristic zero, the endomorphism algebras of the Jacobians of certain superelliptic curves yq=f(x) are products of cyclotomic fields.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=z5ZzOy1K_Ec. 相似文献20.
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