Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra
โ 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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๐ SIMILAR VOLUMES
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
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.