余交换代数上的Drinfeld-Hecke代数
Drinfeld-Hecke algebras over cocommutative algebras
摘要：
若A是一个有余积的余交换代数，则A是一个A-模的对称代数Sym（V）的Smash积代数.这样的Smash积代数，A是群环或李代数，具有变形族，在文献中已经被广泛研究;例子包括辛反射代数和无穷小Hecke代数。我们引入了这类Smash积代数的一族变形，并刻画了PBW性质。然后，我们刻画了“类群”代数（包括群环和nilCoxeter代数）的雅可比恒等式，并精确地识别了例子中的PBW变形，其中A是nilCoxeter代数。最后我们讨论一个更突出的情形--这里A是一个霍普夫代数。证明了Smash积中几种变形关系的等价性，并证明了PBW变形是霍普夫代数.
英文摘要：
If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra Sym(V) with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have families of deformations that have been studied widely in the literature; examples include symplectic reflection algebras and infinitesimal Hecke algebras. We introduce a family of deformations of these smash product algebras for general A, and characterize the PBW property. We then characterize the Jacobi identity for "grouplike" algebras (that include group rings and the nilCoxeter algebra), and precisely identify the PBW deformations in the example where A is the nilCoxeter algebra. We end with the more prominent case - where A is a Hopf algebra. We show the equivalence of several versions of the "deformed" relations in the smash product, and identify the PBW deformations which are Hopf algebras as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
