NDLI: Balanced Deep Matrix Algebras

Content Provider	Springer Nature Link
Author	Kennedy, Christopher
Copyright Year	2010
Abstract	This paper continues the study of associative and Lie deep matrix algebras, ${\mathcal{DM}}(X,{\mathbb{K}})$ and ${\mathfrak{gld}}(X,{\mathbb{K}})$ , and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras, ${\mathcal{BDM}}(X,{\mathbb{K}})$ and ${\mathfrak{bld}}(X,{\mathbb{K}})$ , are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal lattices. In particular, ${\mathfrak{bld}}(X,{\mathbb{K}})$ is shown to be semisimple. The Lie algebra ${\mathfrak{bld}}(X,{\mathbb{K}})$ possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct product of ${\mathfrak{{sl}_n}}$ ’s. We classify all associative bilinear forms on ${\mathfrak{sl}_2\mathfrak{d}}$ (a natural depth analogue of ${\mathfrak{{sl}_2}}$ ) and ${\mathfrak{bld}}$ .
Ending Page	1202
Page Count	16
Starting Page	1187
File Format	PDF
ISSN	1386923X
e-ISSN	15729079
Journal	Algebras and Representation Theory
Issue Number	6
Volume Number	14
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-07-31
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Infinite-dimensional Lie (super) algebras Associative Rings and Algebras Simple, semisimple, reductive (super)algebras Deep matrix algebra Non-associative Rings and Algebras Commutative Rings and Algebras Locally finite Deep Cartan decomposition Ideal lattice Associative symmetric bilinear form
Content Type	Text
Resource Type	Article
Subject	Mathematics

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