发表机构
University of Coimbra（科英布拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对特征零域上的带对合$W$-代数，建立了带对合的$W$-多项式恒等式理论，证明了$(W,*)$-指数与普通$*$-指数一致，并具体分析了四维上三角矩阵子代数的两种不等价结构，计算了其恒等式理想与余维数序列，最终证明它们生成不同的几乎多项式增长簇。
AI 中文摘要
设$W$是特征为零域上的带对合代数。我们利用$A$的带对合乘子代数，为有限维$(W,*)$-代数$A$发展了带对合的$W$-多项式恒等式理论。我们证明了$A$的$(W,*)$-指数存在且与普通$*$-指数一致。然后我们考虑$4\ imes4$上三角矩阵代数的四维子代数$M$，赋予反射对合，并在其上研究两种不等价的$(W,*)$-代数结构。对于这两种结构，我们确定了相应的带对合$W$-多项式恒等式的$T_W^*$-理想，并显式计算了$(W,*)$-余维数序列；对于其中一种结构，我们还确定了完整的$(W,*)$-余特征序列。最后，我们证明了这两个带对合的$W$-代数生成不同的几乎多项式增长簇。
英文摘要
Let $W$ be an algebra with involution over a field of characteristic zero. We develop a theory of $W$-polynomial identities with involution for finite-dimensional $(W,*)$-algebras $A$, using the multiplier algebra with involution of $A$. We prove that the $(W,*)$-exponent of $A$ exists and coincides with the ordinary $*$-exponent. We then consider a four-dimensional subalgebra $M$ of the algebra of $4\times4$ upper triangular matrices, endowed with the reflection involution, and study two non-equivalent $(W,*)$-algebra structures on it. For both structures, we determine the corresponding $T_W^*$-ideals of $W$-polynomial identities with involution and compute the $(W,*)$-codimension sequences explicitly; for one of them, we also determine the complete $(W,*)$-cocharacter sequence. Finally, we prove that these two $W$-algebras with involution generate distinct varieties of almost polynomial growth.
Comments31 pages
