Concept
Polynôme non commutatif
Publications associées (12)
Double Quasi-Poisson Algebras are Pre-Calabi-Yau
In this article, we prove that double quasi-Poisson algebras, which are noncommutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11], where a correspondence between certai ...
2022The Hochschild complex of a twisting cochain
Given any twisting cochain t:C→A , where C is a connected, coaugmented chain coalgebra and A is an augmented chain algebra over an arbitrary commutative ring R, we construct a twisted extension of chain complexes Full-size image (1 K) of which both the wel ...
Elsevier2016The monoid algebra of all relations on a finite set
We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra. ...
2015Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials
This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of t ...
Springer2013Incremental Query Evaluation in a Ring of Databases
This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key prop ...
2013Bar constructions and Quillen homology of modules over operads
We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing ...
2010Vinberg's theta-groups in positive characteristic and Kostant-Weierstrass slices
We generalize the basic results of Vinberg's theta-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We ded ...
Birkhäuser-Verlag, Springer2009Invariant generation for P-solvable loops with assignments
We discuss interesting properties of a general technique for inferring polynomial invariants for a subfamily of imperative loops, called the P-solvable loops, with assignments only. The approach combines algorithmic combinatorics, polynomial algebra and co ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008