Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1403.4172

Type Decomposition in Posets

Tristan Bice
View original source ↗Read source document ↗Export metadata ↓

Abstract

Motivated by the classical type decomposition of von Neumann algebras, and various more recent extensions to other structures, we develop a type decomposition theory for general posets.

Explore related subjects

math.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tristan Bice. 2014-03-17. Type Decomposition in Posets. https://doi.org/10.1515/ms-2016-0202

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On conservative algebras of 2-dimensional Algebras

In 1990 Kantor introduced the conservative algebra $\mathcal{W}(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. In case $n >1$ the algebra $\mathcal{W}(n)$ does not belong to well known classes of algebras (such as associative, Lie, Jordan, Leibniz algebras). We describe $\frac{1}{2}$derivations, local (resp. $2$-local) $\frac{1}{2}$-derivations and biderivations of $\mathcal{W}(2)$. We also study similar problems for the algebra $\mathcal{W}_2$ of all commutative algebras on the two-dimensional vector space and the algebra $\mathcal{S}_2$ of all commutative algebras with trace zero multiplication on the two-dimensional space.

math.RA↗
arXiv2026

Hilbert's Basis Theorem for generalized nonassociative Ore extensions

We introduce a broader class of nonassociative Ore extensions that unifies and generalizes several earlier constructions, taking subadditivity of polynomial degree under multiplication as a guiding principle. We prove generalizations of Hilbert's Basis Theorem for this class, showing that left and right Noetherianity follow from corresponding degree-reduction properties. Applications include flipped nonassociative Ore extensions, mutations, cochain twists, and depolarizations of Poisson Ore extensions.

math.RA↗
arXiv2026

Fixed-point-free automorphisms of solvable Lie algebras

In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie algebra must be even strongly unimodular. We find a necessary and sufficient criterion such that a complex almost abelian Lie algebra admits a fixed-point-free automorphism. For complex filiform Lie algebras we show that the existence of a fixed-point-free automorphism is equivalent to not being characteristically nilpotent.

math.RA↗