Results 1 to 10 of about 24,764 (67)

Dirac Geometry I: Commutative Algebra [PDF]

Peking Mathematical Journal, 2022
The purpose of this paper and its sequel is to develop the geometry built from the commutative algebras that naturally appear as the homology of differential graded algebras and, more generally, as the homotopy of algebras in spectra.
L. Hesselholt, Piotr Pstrągowski
semanticscholar   +1 more source

A commutative algebra approach to multiplicative Hom-Lie algebras [PDF]

Linear and multilinear algebra, 2019
Let be a finite-dimensional complex Lie algebra and be the affine variety of all multiplicative Hom-Lie algebras on . We use a method of computational ideal theory to describe , showing that consists of two 1-dimensional and one 3-dimensional irreducible
Yin Chen, Runxuan Zhang
semanticscholar   +1 more source

Generalizations of Stillman’s Conjecture via Twisted Commutative Algebra [PDF]

International mathematics research notices, 2018
Combining recent results on Noetherianity of twisted commutative algebras by Draisma and the resolution of Stillman’s conjecture by Ananyan–Hochster, we prove a broad generalization of Stillman’s conjecture.
D. Erman, Steven V. Sam, Andrew Snowden
semanticscholar   +1 more source

Hidden constructions in abstract algebra. Krull Dimension of distributive lattices and commutative rings [PDF]

, 2017
We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Espanol and the authors.
T. Coquand, H. Lombardi
semanticscholar   +1 more source

Derivations of Non-Commutative Group Algebras [PDF]

Journal of Algebra and its Applications, 2023
In this article, we study the derivations of group algebras of some important groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral ($SD_{8n}$).
P. Manju, R. Sharma
semanticscholar   +1 more source

Commutative post-Lie algebra structures on Kac–Moody algebras [PDF]

Communications in Algebra, 2018
We determine commutative post-Lie algebra structures on some infinite-dimensional Lie algebras. We show that all commutative post-Lie algebra structures on loop algebras are trivial.
D. Burde, P. Zusmanovich
semanticscholar   +1 more source

Maximal commutative subalgebras of a Grassmann algebra [PDF]

Journal of Algebra and its Applications, 2018
We provide a new approach to the investigation of maximal commutative subalgebras (with respect to inclusion) of Grassmann algebras. We show that finding a maximal commutative subalgebra in Grassmann algebras is equivalent to constructing an intersecting
V. Bovdi, Ho-Hon Leung
semanticscholar   +1 more source

On the pre-commutative envelopes of commutative algebras [PDF]

Journal of Algebra and its Applications
We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation.
H. Alhussein, P. Kolesnikov
semanticscholar   +1 more source

Commutative Algebra: Constructive Methods: Finite Projective Modules [PDF]

, 2015
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra.
H. Lombardi, Claude Quitt'e
semanticscholar   +1 more source

A graded Schur lemma and a graded-monoidal structure for induced modules over graded-commutative algebras [PDF]

Communications in Algebra
We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded generalization of the Schur
Jürgen Fuchs, Tobias Grøsfjeld
semanticscholar   +1 more source