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 ...

2022

The Hochschild complex of a twisting cochain

Kathryn Hess Bellwald

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 ...

Elsevier2016

The monoid algebra of all relations on a finite set

Jacques Thévenaz, Serge Bouc

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. ...

2015

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Sabine Burgdorf

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 ...

Springer2013

Incremental Query Evaluation in a Ring of Databases

Christoph Koch

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 ...

2013

Bar 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 ...

2010

Decision Procedures for Algebraic Data Types with Abstractions

Viktor Kuncak, Philippe Paul Henri Suter, Mirco Dotta

We describe a family of decision procedures that extend the decision procedure for quantifier-free constraints on recursive algebraic data types (term algebras) to support recursive abstraction functions. Our abstraction functions are catamorphisms (term a ...

2010

Vinberg'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, Springer2009

Invariant generation for P-solvable loops with assignments

Laura Ildiko Kovacs

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

Aligator: A mathematica package for invariant generation

Laura Ildiko Kovacs

We describe the new software package Aligator for automatically inferring polynomial loop invariants, The package combines algorithms from symbolic summation and polynomial algebra with computational logic, and is applicable to the rich class of P-solvable ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008

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