منابع مشابه
Family Algebras
A new class of associative algebras is introduced and studied. These algebras are related to simple complex Lie algebras (or root systems). Roughly speaking, they are finite dimensional approximations to the enveloping algebra U(g) viewed as a module over its center. It seems that several important questions on semisimple algebras and their representations can be formulated, studied and sometim...
متن کاملFree pre-Lie algebras are free as Lie algebras
We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.
متن کاملIntroduction to Family Algebras
Classical and quantum family algebras, previously introduced by the author and playing an important role in the theory of semi-smiple Lie algebras and their representations are studied. Basic properties, structure theorems and explicit fomulas are obtained for both types of family algebras in many significant cases. Exact formulas (based on experimental calculations) for quantum eigenvalues, th...
متن کاملFree Algebras in Varieties
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility. In universal algebra we deal with varieties – classes o...
متن کاملAlmost Free Algebras
In this paper we adopt the terminology of universal algebra. So by a free algebra we will mean that a variety (i.e., an equationally defined class of algebras) is given and the algebra is free in that variety. We will also assume that the language of any variety is countable. In this paper the investigation of the almost free algebras is continued. An algebra is said to be almost free if “most”...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2020
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.11.027