On the combinatorics of commutators of Lie algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866911770240614400 |
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| author | Hitomi, Eduardo Yasumura, Felipe |
| author_facet | Hitomi, Eduardo Yasumura, Felipe |
| contents | Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator $[x_1, x_2, ..., x_m]$ as a sum of associative monomials. We characterize this subset and find some useful equivalences. Moreover, we explore properties concerning the action of this subset on sequences of m elements. In particular we describe sequences that share some special symmetries which can be useful in the study of combinatorial properties in graded Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_09407 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On the combinatorics of commutators of Lie algebras Hitomi, Eduardo Yasumura, Felipe Combinatorics Rings and Algebras 17B05, 05E18 Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator $[x_1, x_2, ..., x_m]$ as a sum of associative monomials. We characterize this subset and find some useful equivalences. Moreover, we explore properties concerning the action of this subset on sequences of m elements. In particular we describe sequences that share some special symmetries which can be useful in the study of combinatorial properties in graded Lie algebras. |
| title | On the combinatorics of commutators of Lie algebras |
| topic | Combinatorics Rings and Algebras 17B05, 05E18 |
| url | https://arxiv.org/abs/1609.09407 |