Results 81 to 90 of about 145 (139)
Multiplier Infinitesimal Bialgebras and Derivator Lie Bialgebras
, 2011 11 ...
Arango, Jesus Alonso Ochoa +2 more
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Transactions of the American Mathematical Society, 2015 A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the ‘base algebras’) are shown to carry coseparable co-Frobenius coalgebra structures.
Böhm, Gabriella Eszter +2 more
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A Pairing Theorem between a Braided Bialgebra and Its Dual Bialgebra
Journal of Algebra, 2001 Let \(q\in\mathbb{C}\setminus\{0\}\) and \(R=\sum^n_{i,j=1}q^{i-j}E_{ii}\otimes E_{jj}\) be a special Hayashi \(R\)-matrix, where \(E_{ii}\) are matrix units. Then \(R\) is an \(n^2\times n^2\) \(R\)-matrix, and one can construct the FRT bialgebra \(A_R\) over \(\mathbb{C}\), which is an infinite dimensional braided bialgebra determined by the ...
Maozheng, Guo +2 more
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The purpose of this paper is to construct infinite-dimensional Poisson bialgebras by the affinization of pre-Poisson algebras. There is a natural Poisson algebra structure on the tensor product of a pre-Poisson algebra and a perm algebra, and the Poisson algebra structure on the tensor product of a pre-Poisson algebra and a special perm algebra ...
Guo, Yanhong, Hou, Bo
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Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
, 2010 We study the Hom-type generalization of infinitesimal bialgebras, called infinitesimal Hom-bialgebras. In particular, we consider infinitesimal Hom-bialgebras arising from quivers, the sub-classes of coboundary and quasi-triangular infinitesimal Hom-bialgebras, the associative Hom-Yang-Baxter equation, and homological perturbation of the ...
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Advances in Applied Mathematics, 2008 An infinite magmatic bialgebra is a vector space endowed with an n-ary operation, and an n-ary cooperation, for each n, verifying some compatibility relations. We prove a rigidity theorem, analogue to the Hopf-Borel theorem for commutative bialgebras: any connected infinite magmatic bialgebra is of the form $Mag^\infty(Prim H)$, where $Mag^\infty(V ...
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PENTAGON EQUATION AND MATRIX BIALGEBRAS [PDF]
Communications in Algebra, 2001 We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the non-unitary case. We establish the relation between Hopf-Galois algebras and solutions to modified pentagon equation.
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A combinatorial PROP for bialgebras
European Journal of Combinatorics30 pages, 5 ...
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On Poisson Conformal Bialgebras
Algebras and Representation Theory30 ...
Yanyong Hong, Chengming Bai
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Infinite-dimensional Lie bialgebras via affinization of perm bialgebras and pre-Lie bialgebras
Journal of AlgebraIt is known that the operads of perm algebras and pre-Lie algebras are the Koszul dual each other and hence there is a Lie algebra structure on the tensor product of a perm algebra and a pre-Lie algebra. Conversely, we construct a special perm algebra structure and a special pre-Lie algebra structure on the vector space of Laurent polynomials such that
Yuanchang Lin, Peng Zhou, Chengming Bai
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