Search arXiv⌕ Search

arXiv · 0704.2411

Indecomposable invariants of quivers for dimension (2,...,2) and maximal paths

Abstract

An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the reduction to the problem of description of maximal paths satisfying certain condition.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. A. Lopatin. 2010-04-26. Indecomposable invariants of quivers for dimension (2,...,2) and maximal paths. https://arxiv.org/abs/0704.2411

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

KEEP EXPLORING

Related papers

Multilinear nilalgebras and the Jacobian theorem

If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed by Dotsenko.

math.RA↗

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

In this paper, we study local superderivations and local anti-superderivations of finite-dimensional nilpotent Lie superalgebras over a field $\mathbb F$ with $\operatorname{char}\mathbb F\neq2$. First, we prove that every finite-dimensional two-step nilpotent Lie superalgebra admits pure local superderivations and pure local anti-superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). For nilpotent Lie superalgebras of nilpotency index greater than two, we establish sufficient conditions for the existence of pure local superderivations and pure local anti-superderivations. In particular, we prove that every three-step nilpotent Lie superalgebra admits a pure local superderivation.

math.RA↗