On the combinatorics of commutators of Lie algebras
2019 ◽
Vol 19
(06)
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pp. 2050119
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 [Formula: see text] 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 [Formula: see text] 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.
2009 ◽
Vol 164
(2)
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pp. 250-254
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2020 ◽
Vol 24
(12)
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pp. 360-396
1992 ◽
pp. 120-137
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Keyword(s):
1997 ◽
Vol 349
(10)
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pp. 4021-4051
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2020 ◽
Vol 90
(1)
◽
pp. 45-71