An existence condition for multilinear quantum operations
type: Item
instance of: scholarly article
title: An existence condition for multilinear quantum operations
zbMATH Open document ID: 0943.17016
published in: Journal of Algebra
publication date: 2000-09-06T00:00:00Z
review text: Recall that a quantum variable is a variable \(x\), with which an element \(g_x\) of a fixed abelian group \(G\) and a character \(\chi^ x: G \rightarrow k^*\) are associated. In this paper the author shows that there exists a non-zero multilinear quantum operation in a set of quantum variables \(x_1, x_2, \cdots , x_n\) if and only if this set is conforming, i.e., \[ \prod_{1\leq i\neq j\leq n}\chi^{x_i}(g_{x_j})=1. \] Moreover, he proves that if the set \(x_1, x_2, \cdots , x_n\) has no proper conforming subset, then the dimension of the space of all multilinear quantum operation in \(x_1, x_2, \cdots , x_n\) equals \((n-2)!\).
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1340610
zbMATH Keywords: quantum group
zbMATH Keywords: multilinear quantum operation
zbMATH Keywords: quantum variable
author: V. K. Kharchenko
MaRDI profile type: Publication
full work available at URL: jabr.1998.7798
OpenAlex ID: W1993380097
cites work: Q4343354
cites work: Q4242303
cites work: Skew derivations of prime rings
cites work: Q4002121
cites work: Q3236717
cites work: Q5569204
DOI: 10.1006/JABR.1998.7798
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description: scientific article; zbMATH DE number 1340610