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Finitely presented infinite-dimensional simple Lie algebras

โœ Scribed by Ian Stewart


Book ID
112500837
Publisher
Springer
Year
1975
Tongue
English
Weight
175 KB
Volume
26
Category
Article
ISSN
0003-889X

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Finitely Presented Lie Algebras
โœ R.M. Bryant; J.R.J. Groves ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 179 KB
Some non-finitely presented Lie algebras
โœ Joseph Abarbanel; Shmuel Rosset ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 493 KB

Let L be a free Lie algebra over a field k, I a non-trivial proper ideal of L, n > 1 an integer. ## The multiplicator Hz(L/I",R) of L/I" is not finitely generated, and so in particular, L/Z" is not finitely presented, even when L/I is finite dimensional.

Construction of Finitely Presented Lie A
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We consider the following problem: what is the most general Lie algebra or superalgebra satisfying a given set of Lie polynomial equations? The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of

New Simple Infinite-Dimensional Lie Alge
โœ J.Marshall Osborn ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 198 KB

We construct here several classes of simple Lie algebras of characteristic ลฝ . 0 which include the Virasoro algebra without central charge and the graded Lie algebras of Cartan type. Our construction is motivated by our w x recent construction of simple locally Novikov algebras in 5 . Our simple Li