搜索结果: 1-15 共查到“代数学 Hopf algebras”相关记录23条 . 查询时间(0.05 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
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2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
Basic Hopf Algebras of Finite Representation Type and Their Classification
Basic Hopf Algebras Finite Representation Type Their Classification
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2018/4/20
Let k be a algebraically closed field. We give a necessary and sufficient condition for a basic Hopf algebra over k to be finite representation type. Explicitly, we prove that a basic Hopf algebra ove...
Hopf Algebras and Tensor Categories
Hopf Algebras Tensor Categories
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2016/7/18
Options of traveling to Nankai University NOTE: On Sept 4, CIM will organize 3 buses to Beijing airport to pick up the participants (morning, noon and evening). Once you book your flight, please let...
GALOIS CONNECTIONS FOR INCIDENCE HOPF ALGEBRAS OF PARTIALLY ORDERED SETS.
Incidence Hopf algebras Galois connections
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2015/8/14
An important well-known result of Rota describes the relationship between the M¨obius
functions of two posets related by a Galois connection. We present an analogous result relating
the antipodes of...
Infinitesimal Hopf algebras
Hopf algebras derivations Yang-Baxter equation Drinfeld’s double
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2015/8/14
Infinitesimal bialgebras were introduced by Joni and Rota [J-R].
An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in
such a way that the comultiplication is a derivation. I...
Representations of matched pairs of groupoids and applications to weak Hopf algebras
groupoids and applications algebras
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2015/8/14
We introduce the category of set-theoretic representations of a
matched pair of groupoids. This is a monoidal category endowed with a
monoidal functor f` to the category of quivers over the common b...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
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2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...
COMBINATORIAL HOPF ALGEBRAS AND GENERALIZED DEHN-SOMMERVILLE RELATIONS
Hopf algebra, character, generalized Dehn-Sommerville relations
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2015/8/14
A combinatorial Hopf algebra is a graded connected Hopf algebra over
a field k equipped with a character (multiplicative linear functional) : H → k.
We show that the terminal object in the categor...
Coxeter groups and Hopf algebras I
Coxeter group descent global descent hyperplane arrangement
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2015/8/14
In the study of a mathematical system, algebraic structures allow for the discovery of
more information. This is the motor behind the success of many areas of mathematics
such as algebraic geometry,...
Hopf algebras and Markov chains: Two examples and a theory
By-products hopf algebra markov chain complex lie algebra combination
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2015/7/7
The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied meth...
On the structure of cofree Hopf algebras
cofree Hopf algebras
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2015/3/25
We prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B-infini-algeb...
Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit
Hochschild homology of Hopf algebras free Yetter-Drinfeld resolutions the counit K-Theory and Homology
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2012/4/18
We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter-Drinfeld resolution of the counit of $A$ to the sam...
Twisted Frobenius-Schur indicators for Hopf algebras
semisimple Hopf algebra character Frobenius–Schur indicator automorphism
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2011/8/25
Abstract: The classical Frobenius-Schur indicators for finite groups are character sums defined for any representation and any integer m greater or equal to 2. In the familiar case m=2, the Frobenius-...
A PBW basis criterion for pointed Hopf algebras
PBW pointed Hopf algebras
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2010/11/8
We give a necessary and sufficient PBW basis criterion for Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of ...
Lie-Hopf algebras and loop homology of suspension spaces
Lie-Hopf algebras loop homology suspension spaces
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2010/11/18
For an arbitrary topological space $X$, the loop space homology $H_*(\Omega\Sigma X; \mathbb{Z})$ is a Hopf algebra. We introduce a new homotopy invariant of a topological space $X$ that takes values...