扭曲的超Yangian代数的准分裂型A
Twisted super Yangians of quasi-split type A
AI总结：
本文研究了准分裂型A的扭曲超Yangian代数，通过Gauss分解证明其与特殊扭曲超Yangian同构，并推广了非超情况下的已知结果。
AI中文摘要：
我们介绍了一个任意对称奇性序列$\mathfrak{s}$的扭曲超Yangian$Y^{\mathfrak{s}}_{\imath}$的Drinfeld电流表示。通过Gauss分解证明$Y^{\mathfrak{s}}_{\imath}$与特殊的扭曲超Yangian$\mathscr{SY}^{\mathfrak{s}}$同构，后者是之前通过R矩阵表示定义的扭曲超Yangian$\mathscr{Y}^{\mathfrak{s}}$的子代数。作为推论，我们显示对应于不同对称奇性序列但具有相同$\mathfrak{m}$和$\mathfrak{n}$的$Y^{\mathfrak{s}}_{\imath}$代数是同构的。我们还为$Y^{\mathfrak{s}}_{\imath}$建立了PBW定理，并以Gaussian生成元的形式描述$\mathscr{Y}^{\mathfrak{s}}$的中心，从而推广了非超准分裂型A情况下的已知结果。
英文摘要：
We introduce the twisted super Yangian $Y^{\mathfrak{s}}_{\imath}$ of quasi-split type A in the Drinfeld current presentation for an arbitrary symmetric parity sequence $\mathfrak{s}$. We prove via Gauss decomposition that $Y^{\mathfrak{s}}_{\imath}$ is isomorphic to the special twisted super Yangian $\mathscr{SY}^{\mathfrak{s}}$, a subalgebra of the twisted super Yangian $\mathscr{Y}^{\mathfrak{s}}$ previously defined via the R-matrix presentation. As a corollary, we show that the algebras $Y^{\mathfrak{s}}_{\imath}$ corresponding to different symmetric parity sequences with the same $\mathfrak{m}$ and $\mathfrak{n}$ are isomorphic. We also establish a PBW theorem for $Y^{\mathfrak{s}}_{\imath}$ and describe the center of $\mathscr{Y}^{\mathfrak{s}}$ in terms of Gaussian generators, thereby generalizing known results for the nonsuper quasi-split type A case.
