Poincaré Lemma for a quasibraided Heisenberg algebra
Abstract
A quasi-braided algebra is an algebra $A$ on a commutative ring $\L$ with unit, equipped with an operator $R\in\End(A\otimes A)$ which satisfaces the Yang-Baxter equation, $R(1\otimes a)=a\otimes1$ and $R(a\otimes1)=1\otimes a$. The quasi-braided differential calculus $\Omega_{R}(A)$ is obtained from the universal differential calculus modulo the relations $a\,db=\sum_i(db^i)a_i$, donde $R(a\otimes b)= \sum_ia_i\otimes b_i$. We show a version of Poincaré's Lemma for a quasibraided Heisenberg algebra on $\mathbb{R}[x]$.
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