35 citations · 76 across the 27 of their papers we have counts for
27 papers
Double cross products with projections and relative Rota-Baxter operators on Hopf algebras
Yunnan Li
Given a matched pair of Hopf algebras, the double cross product construction yields a new Hopf algebra, the prototypical example of which is the generalized quantum double arising…
On restricted Rota-Baxter Lie algebras of arbitrary weight
Yunnan Li, Ke Ou
Recently, Ehret and Gilliers introduced the notion of a (trivially) restricted post-Lie algebra, recovering the concepts of a restricted Lie algebra and a restricted pre-Lie algebr…
Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration
Adrien Busnot Laurent, Yunnan Li, Yunhe Sheng
In this paper, we introduce the notion of post-Hopf algebroids, generalizing the pre-Hopf algebroids introduced in [Bronasco, Laurent, 2025] in the study of exotic aromatic S-serie…
Generalized Reynolds algebras from Volterra integrals and their free construction by complete shuffle product
Li Guo, Richard Gustavson, Yunnan Li
This paper introduces algebraic structures for Volterra integral operators with separable kernels, in the style of differential algebra for derivations and Rota-Baxter algebra for…
On the sub-adjacent Hopf algebra of the universal enveloping algebra of a post-Lie algebra
Yunnan Li
Recently the notion of post-Hopf algebra was introduced, with the universal enveloping algebra of a post-Lie algebra as the fundamental example. A novel property is that any cocomm…
Categorification of based modules over the complex representation ring of
Wenxia Wu, Yunnan Li
The complex representation rings of finite groups are the fundamental class of fusion rings, categorified by the corresponding fusion categories of complex representations. The cat…
Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and -structures
Yunnan Li, Yunhe Sheng, Rong Tang
In this paper, we study relative Rota-Baxter operators of weight on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operat…
Towards the classification of finite-dimensional diagonally graded commutative algebras
Yunnan Li, Shi Yu
Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic…
Cohomologies of difference Lie groups and van Est theorem
Jun Jiang, Yunnan Li, Yunhe Sheng
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce…
Primitive decompositions of idempotents of the group algebras of dihedral groups and generalized quaternion groups
Lilan Dai, Yunnan Li
In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn…
Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
Yunnan Li, Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf al…
Crossed homomorphisms and Cartier-Kostant-Milnor-Moore theorem for difference Hopf algebras
Li Guo, Yunnan Li, Yunhe Sheng +1
The celebrated Milnor-Moore theorem and the more general Cartier-Kostant-Milnor-Moore theorem establish close relationships of a connected and a pointed cocommutative Hopf algebra…
Construction of free differential algebras by extending Gröbner-Shirshov bases
Li Guo, Yunnan Li
As a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known…
An algebraic study of Volterra integral equations and their operator linearity
Li Guo, Richard Gustavson, Yunnan Li
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an al…
Coherent unit actions on braided operads and Hopf algebras
Li Guo, Yunnan Li
The notion of a coherent unit action on algebraic operads was first introduced by Loday for binary quadratic nonsymmetric operads and generalized by Holtkamp, to ensure that the fr…
Cohomologies, extensions and deformations of differential algebras with any weights
Li Guo, Yunnan Li, Yunhe Sheng +1
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has…
Braided dendriform and tridendriform algebras and braided Hopf algebras of planar trees
Li Guo, Yunnan Li
This paper introduces the braidings of dendriform algebras and tridendriform algebras. By studying free braided dendriform algebras, we obtain braidings of the Hopf algebras of Lod…
Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras
Li Guo, Yunnan Li
Rota-Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures prov…
On weak peak quasisymmetric functions
Yunnan Li
In this paper, we construct the weak version of peak quasisymmetric functions inside the Hopf algebra of weak composition quasisymmetric functions (WCQSym) defined by Guo, Thibon a…
The distance spectra of the derangement graphs
Yunnan Li, Huiqiu Lin
In this paper, we consider the distance spectra of the derangement graphs. First we give a constructive proof that the connected derangement graphs are of diameter 2. Then we obtai…
Towards a polynomial basis of the algebra of peak quasisymmetric functions
Yunnan Li
Hazewinkel proved the Ditters conjecture that the algebra of quasisymmetric functions over the integers is free commutative by constructing a nice polynomial basis. In this paper w…
Representation theory of 0-Hecke-Clifford algebras
Yunnan Li
The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothen…
The shifted Poirier-Reutenauer algebra
Naihuan Jing, Yunnan Li
Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur's P-functions and a ri…
A lift of Schur's Q-functions to the peak algebra
Naihuan Jing, Yunnan Li
We construct a lift of Schur's Q-functions to the peak algebra of the symmetric group, called the noncommutative Schur Q-functions, and extract from them a new natural basis with s…