论文标题
量子Borcherds-bozec代数的经典限制
Classical limit of quantum Borcherds-Bozec algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为borcherds-bozec代数，$ u（\ mathfrak {g}）$为其通用包围的代数和$ u_ {q}（\ mathfrak {g}）$是相应的量子量子borcherds-bozec-bozec algebra。我们表明，$ u_ {q}的经典限制（\ mathfrak {g}）$是$ u（\ mathfrak {g}）$作为hopf代数。因此，$ u_ {q}（\ mathfrak {g}）$可以被视为$ u（\ mathfrak {g}）$的量子变形。我们还为$ u_ {q}（\ mathfrak {g}）$的发电机之间的换向关系提供了明确的公式。
Let $\mathfrak{g}$ be a Borcherds-Bozec algebra, $U(\mathfrak{g})$ be its universal enveloping algebra and $U_{q}(\mathfrak{g})$ be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of $U_{q}(\mathfrak{g})$ is isomorphic to $U(\mathfrak{g})$ as Hopf algebras. Thus $U_{q}(\mathfrak{g})$ can be regarded as a quantum deformation of $U(\mathfrak{g})$. We also give explicit formulas for the commutation relations among the generators of $U_{q}(\mathfrak{g})$.
