Results 71 to 80 of about 145 (139)
Novel non‐involutive solutions of the Yang–Baxter equation from (skew) braces
Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.Abstract We produce novel non‐involutive solutions of the Yang–Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces, they are not necessarily involutive.
Anastasia Doikou, Bernard Rybołowicz
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Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory
MathematicsA left-Alia algebra is a vector space together with a bilinear map satisfying the symmetric Jacobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce the notions of
Chuangchuang Kang +3 more
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Near braces and p$p$‐deformed braided groups
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 124-139, January 2024.Abstract Motivated by recent findings on the derivation of parametric noninvolutive solutions of the Yang–Baxter equation, we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi‐parametric, nondegenerate, noninvolutive solutions of the set‐theoretic Yang–Baxter equation.
Anastasia Doikou, Bernard Rybołowicz
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Bialgebraic Structures And Smarandache Bialgebraic Structures
, 2003 The study of bialgebraic structures started very recently. Till date there are no books solely dealing with bistructures. The study of bigroups was carried out in 1994-1996. Further research on bigroups and fuzzy bigroups was published in 1998. In the year 1999, bivector spaces was introduced.
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Equivariant resolutions over Veronese rings
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract Working in a polynomial ring S=k[x1,…,xn]$S={\mathbf {k}}[x_1,\ldots ,x_n]$, where k${\mathbf {k}}$ is an arbitrary commutative ring with 1, we consider the d$d$th Veronese subalgebras R=S(d)$R={S^{(d)}}$, as well as natural R$R$‐submodules M=S(⩾r,d)$M={S^{({\geqslant r},{d})}}$ inside S$S$.
Ayah Almousa +4 more
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Differential Antisymmetric Infinitesimal Bialgebras, Coherent Derivations and Poisson Bialgebras
Symmetry, Integrability and Geometry: Methods and Applications, 2023 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.
Lin, Yuanchang +2 more
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پژوهشهای ریاضی, 2020 Introduction Over a commutative ring k, it is well known from the classical module theory that the tensor-endofunctor of is left adjoint to the Hom-endofunctor. The unit and counit of this adjunction is obtained trivially.
Saeid Bagheri
doaj
Lie bialgebras constructed from Zinbiel bialgebras and Leibniz bialgebras
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 ...
Hou, Bo, Lin, Yuanchang
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Preantipodes for dual quasi-bialgebras [PDF]
Israel Journal of Mathematics, 2012 It is known that a dual quasi-bialgebra with antipode $H$, i.e. a dual quasi-Hopf algebra, fulfils a fundamental theorem for right dual quasi-Hopf $H$-bicomodules. The converse in general is not true. We prove that, for a dual quasi-bialgebra $H$, the structure theorem amounts to the existence of a suitable map $S:H\rightarrow H$ that we call a ...
ARDIZZONI, Alessandro, PAVARIN, Alice
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Small bialgebras with a projection
Journal of Algebra, 2007 Let \(A\) be a bialgebra over a field \(K\) of characteristic zero, \(H\) a subbialgebra with antipode, such that there is a coalgebra projection \(p\) of \(A\) onto \(H\). Let \(R\) be the \(H\)-coinvariant part of \(A\), i.e., the elements \(a\) in \(A\) so that \(\sum a_1\otimes p(a_2)=a\otimes 1\). The authors determine the structure of \(A\) when \
ARDIZZONI, Alessandro +2 more
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