182 citations · 433 across the 14 of their papers we have counts for
14 papers
Free resolutions constructed from bigradings on Lie algebras
Xianglong Ni, Jerzy Weyman
We construct two families of free resolutions that resolve the ideals of certain opposite Schubert varieties restricted to the big open cell. We conjecture that these examples have…
The InvariantRing package for Macaulay2
Luigi Ferraro, Federico Galetto, Francesca Gandini +3
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of fini…
The Bracket in the Bar Spectral Sequence for an Iterated Loop Space
Xianglong Ni
When is an associative H-space, the bar spectral sequence computes the homology of the delooping, . If is an -fold loop space for this is a spectral…
Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications
Matilde Marcolli, Xiang Ni
We consider Rota-Baxter algebras of meromorphic forms with poles along a (singular) hypersurface in a smooth projective variety and the associated Birkhoff factorization for algebr…
Generalizations of the classical Yang-Baxter equation and O-operators
Chengming Bai, Xiang Ni, Li Guo
Tensor solutions (-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the -matrix solution of the quantum Yang-Baxter…
Replicating of binary operads, Koszul duality, Manin products and average operators
Jun Pei, Chengming Bai, Li Guo +1
We consider the notions of the replicators, including the duplicator and triplicator, of a binary operad. As in the closely related notions of di-Var-algebra and tri-Var-algebra in…
Splitting of operations, Manin products and Rota-Baxter operators
Chengming Bai, Olivia Bellier, Li Guo +1
This paper provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin pro…
L-quadri-algebras
Ligong Liu, Xiang Ni, Chengming Bai
Quadri-algebras introduced by Aguiar and Loday are a class of remarkable Loday algebras. In this paper, we introduce a notion of L-quadri-algebra with 4 operations satisfying certa…
Some results on L-dendriform algebras
Chengming Bai, Ligong Liu, Xiang Ni
We introduce a notion of L-dendriform algebra due to several different motivations. L-dendriform algebras are regarded as the underlying algebraic structures of pseudo-Hessian stru…
Special symplectic Lie groups and hypersymplectic Lie groups
Xiang Ni, Chengming Bai
A special symplectic Lie group is a triple such that is a finite-dimensional real Lie group and is a left invariant symplectic form on which is parallel…
O-operators on associative algebras and dendriform algebras
Chengming Bai, Li Guo, Xiang Ni
An O-operator is a relative version of a Rota-Baxter operator and, in the Lie algebra context, is originated from the operator form of the classical Yang-Baxter equation. We genera…
Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
Xiang Ni, Chengming Bai, Li Guo
We generalize the classical study of (generalized) Lax pairs and the related -operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabeli…
-operators on associative algebras and associative Yang-Baxter equations
Chengming Bai, Li Guo, Xiang Ni
We introduce the concept of an extended O-operator that generalizes the well-known concept of a Rota-Baxter operator. We study the associative products coming from these operators…
Pre-alternative algebras and pre-alternative bialgebras
Xiang Ni, Chengming Bai
We introduce a notion of pre-alternative algebra which may be seen as an alternative algebra whose product can be decomposed into two pieces which are compatible in a certain way.…