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Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra

โœ Scribed by A. A. Dosiev


Book ID
110430050
Publisher
Springer US
Year
2003
Tongue
English
Weight
115 KB
Volume
37
Category
Article
ISSN
0016-2663

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๐Ÿ“œ SIMILAR VOLUMES


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โœ Roy Meshulam; Nizar Radwan ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 235 KB

Let 9 be a complex semi-simple Lie algebra. Extending a result of Gerstenhaber on spaces of nilpotent matrices, it is shown that if W c g is a linear subspace of ad nilpotent elements then dim W < i( dim.g -rank g). Similarly, it is shown that the maximal dimension of a linear space of symmetric nil

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We find an explicit formula for the total dimension of the homology of a free 2-step nilpotent Lie algebra. We analyse the asymptotics of this formula and use it to find an improved lower bound on the total dimension of the homology of any 2-step nilpotent Lie algebra.