article · 2006
10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV
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Abstract
Abstract. Skew-symmetric sum of N! compositions of N vector fields in all possible order is called N-commutator. We construct 10-commutator and 13-commutator on V ect(3) and 10-commutator on a space of divergenceless vector fields V ect0(3). We show that 2-commutator, 10-commutator and 13-commutator form final list of N-commutators on V ect(3) and under these polylinear operations V ect(3) has a structure of sh-Lie algebra. We establish that the list of 2-and 10-commutators on V ect0(3) is also final. Constructions are based on calculations of powers of odd derivations. Let (A, ◦) be an algebra with vector space A and multiplication ◦. Let C < t1,..., tk> be a space of non-commutative non-associative polynomials. Any f ∈ C < t1,..., tk> induces a k-ary map f: A × · · · × A → A, k that corresponds to any a1,..., ak ∈ A element f(a1,..., ak) calculated in terms of multiplication ◦. If this map is trivial, i.e., f(a1,..., ak) = 0, for any a1,..., ak ∈ A then f = 0 is said an identity on (A, ◦). If f is polylinear, then f induces a k-ary multiplication on A. For example, if s2 = t1t2 − t2t1 ∈ C < t1, t2>, then s2(a, b) = a ◦ b − b ◦ a is an ordinary commutator.
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(2006). 10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV.
“10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV.” 2006.
2006. “10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV.”
(2006) ‘10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV’.
@article{anon2006commutator,
title = {{10-COMMUTATOR AND 13-COMMUTATOR A.S. DZHUMADIL’DAEV}},
year = {2006}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.