منابع مشابه
Commutators of Skew-Symmetric Matrices
In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g an...
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In the paper we consider some commutator-type and power-type matrix equations in the group UT(∞,K) of infinite dimensional unitriangular matrices over a fieldK. We introduce a notion of a power outer commutator ω1k k (x1, ..., xk) and a power Engel commutator e1k k (x, y) as outer (respectively Engel) commutators modified by allowing powers of letters instead of letters alone. For a given infin...
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Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived. Gamma matrix algebra is ubiquitous in many calculations in high energy physics. Whereas it is a fairly simple business in four dimensions, in higher-dimensional applications such as supergravity or M-theory, it becomes quite involved, because the number of independent matrices grow...
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This note will be for the most part of an expository nature; many of the results here have appeared elsewhere. We would like however, to highlight the connection between Jim Stasheff’s early work on A∞ algebras in the 1960’s and the notion of sh Lie algebras (L∞ algebras) which is currently popular in mathematical physics; see, for example, [1] and [7]. This connection involves some work of Vic...
متن کاملA Strange Phenomenon for the Singular Values of Commutators with Rank One Matrices∗
The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2014
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1604