Results 81 to 90 of about 1,412 (138)
, 2021 An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives an equivalent presentation with only one operation for a Poisson algebra. We establish a bialgebra theory for adm-Poisson algebras independently and systematically, including but ...
Liang, Jinting +2 more
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Some Properties of Birings [PDF]
, 2013 Generally speaking, the unions of any two subgroups of a group, subgroupoids of a groupoid, subsemigroups of a semigroup, submonoids of a monoid, subloops of a loop, subsemirings of a semiring, subfields of a field and subspaces of a vector space do not ...
Agbola, A.A.A.
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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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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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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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Rota–Baxter cosystems and coquasitriangular mixed bialgebras
, 2020 International audienceIn this paper, we present a dual version of T. Brzeziński’s results about Rota–Baxter systems which appeared in [Rota–Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra 460 (2016) 1–25].
Silvestrov, Sergei, +5 more
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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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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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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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