“…Similar commutation relations are known from the theory of alternative algebras [10]. This is due to the fact that the commutator algebras of alternative algebras are the Mal'tsev algebras.…”
The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.
“…Similar commutation relations are known from the theory of alternative algebras [10]. This is due to the fact that the commutator algebras of alternative algebras are the Mal'tsev algebras.…”
The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.
“…Since W 2 = 0, we have that A/W and W are solvable. Therefore, from Schafer [3] (Proposition 2.2, p.18), we get that A is solvable, which proves Theorem 5. The proof of Zelmanov and Skosyrskii [5] uses characteristic 6 = 2, 3, 5.…”
We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Our main result is that these algebras are solvable and not necessarily nilpotent. Our results require characteristic 6 = 2, 3, 5.2000 Mathematics Subject Classification : 17 A30.
“…Theorem 2 follows from the next general theorem (Cf, [3]). But in our case the trace form is positive definite so the proof of Theorem 2 is easy as we shall see in §3.…”
Section: φ'Kv Q) = H'-kv C) π H 2i (V Q) mentioning
Let V be a compact nonsingular algebraic variety of dimension n with a Hodge structure ω and let Hi,i(V,C) be the subgroup of 2i-th cohomology group H2i(V,C) represented by harmonic (i,i)-forms on V with respect to ω.
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