Results 11 to 20 of about 1,418 (162)
GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS [PDF]
Glasgow Mathematical Journal, 2013 AbstractMalvenuto and Reutenauer (C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra177 (1995), 967–982) showed how the total symmetric group ring ⊕nZΣn could be made into a Hopf algebra with a very nice structure which admitted the Solomon descent algebra as a sub-Hopf algebra.
Martin D. Crossley
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Differential Antisymmetric Infinitesimal Bialgebras, Coherent Derivations and Poisson Bialgebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2022 We establish a bialgebra theory for differential algebras, called differential antisymmetric infinitesimal (ASI) bialgebras by generalizing the study of ASI bialgebras to the context of differential algebras, in which the derivations play an important role.
Yuanchang Lin +2 more
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A new branch of bialgebraic structures: UP-bialgebras [PDF]
Journal of Taibah University for Science, 2019 The notion of bialgebraic structures was discussed by Vasantha Kandasamy [Bialgebraic structures and Smarandache bialgebraic structures. India: American Research Press; 2003]. The main target of this paper is to introduce the notions of a KU-bialgebra, a
Phakawat Mosrijai, Aiyared Iampan
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Lie bialgebras constructed from Zinbiel bialgebras and Leibniz bialgebras [PDF]
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend such conclusion to the context of bialgebras. We show that there is a Lie bialgebra structure on the tensor product of a Leibniz bialgebra and a quadratic ...
Bo Hou, Yuanchang Lin
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Annales de l'Institut Fourier, 2011 The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always ...
Marı́a Ronco
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Quantization of Lie bialgebras, IV [PDF]
Selecta Mathematica, 1998 40 pages, amstex. The new version contains several changes throughout the paper suggested by the referee of Selecta Math. In particular, Chapter 10 (functoriality of quantization) is completely rewritten to make the exposition more clear and precise; the May 2016 version points out an error in the proof of Prop. 9.7 found by A.
Pavel Etingof, David Kazhdan
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Partial magmatic bialgebras [PDF]
Homology, Homotopy and Applications, 2007 A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are subsets of the set of positive integers, is a vector space endowed with an n-ary operation for each n in S and an m-ary co-operation for each m in T satisfying some compatibility and unitary relations.
Emily Burgunder, Ralf Holtkamp
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Electronic Notes in Theoretical Computer Science, 2010 AbstractWe study bialgebras in the compact closed category Rel of sets and binary relations. We show that various monoidal categories with extra structure arise as the categories of (co)modules of bialgebras in Rel. In particular, for any group G we derive a ribbon category of crossed G-sets as the category of modules of a Hopf algebra in Rel which is ...
Masahito Hasegawa
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Lie 2-bialgebras: the strict case [PDF]
Communications in Mathematical Physics, 2011 22 ...
Chengming Bai +2 more
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Atiyah classes of three-dimensional Lie bialgebras over Z_3
四川大学学报. 自然科学版, 2019 Based on the theory of Lie algebra cohomology and the definition of the Atiyah class of a Lie bialgebra, Atiyah classes of all three-dimensional Lie bialgebras over Z_3 are calculated.
SHEN Dan-Dan
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