Group identities on the units of algebraic algebras with applications to restricted enveloping algebras
نویسندگان
چکیده
An algebra A is called a GI-algebra if its group of units A satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite? 2000Mathematics Subject Classification. 16R40; 16R50; 16U60; 17B35.
منابع مشابه
Product preservation and stable units for reflections into idempotent subvarieties
We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...
متن کاملSimilarity DH-Algebras
In cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...
متن کاملTransfer of Ideals and Quantization of Small Nilpotent Orbits
We introduce and study a transfer map between ideals of the universal enveloping algebras of two members of a reductive dual pair of Lie algebras. Its definition is motivated by the approach to the real Howe duality through the theory of Capelli identities. We prove that this map provides a lower bound on the annihilators of theta lifts of representations with a fixed annihilator ideal. We also...
متن کاملDrinfeld Orbifold Algebras
We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection algebras, and universal enveloping algebras of Lie algebras with group actions. We giv...
متن کاملA new approach to characterization of MV-algebras
By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007