Abstract
We study the behaviour of contact brackets on the tensor product of two algebras, in particular, address the question of Martínez and Zelmanov about extension of a contact bracket on the tensor product from the brackets on the factors.
Acknowledgments
Thanks are due to Ivan Kaygorodov for pointing out some relevant literature. GAP [Citation14] was used to check some of the computations performed in this note.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 Of course, this is just a manifestation of the vector space isomorphism C2(A ⊗ B) ≃ C2(A) ⊗ S2(B) + S2(A) ⊗ C2(B), where C2 and S2 denote the vector space of anticommutative and commutative brackets on the corresponding algebra, respectively. However, we use a similar reasoning in more complicated situations, where the argument based on the above decomposition of C2(A ⊗ B) is not enough.
2 Note that Remark 5.1.1(2) in [Citation5], which claims the contrary, is incorrect.