Lipschitz property for systems of linear mappings and bilinear forms
Representation Theory
2019-03-26 v1
Abstract
Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge. Two representations A and A' of G are called isomorphic if there is a system of linear bijections between the vector spaces corresponding to the same vertices that transforms A to A'. We prove that if two representations are isomorphic and close to each other, then their isomorphism can be chosen close to the identity.
Keywords
Cite
@article{arxiv.1903.10386,
title = {Lipschitz property for systems of linear mappings and bilinear forms},
author = {Abdullah Alazemi and Milica Anđelić and Carlos M. da Fonseca and Vladimir V. Sergeichuk},
journal= {arXiv preprint arXiv:1903.10386},
year = {2019}
}
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12 pages