A note on parabolic Verma module homomorphisms over Kac-Moody algebras
نویسندگان
چکیده
We consider a general parabolic category OS over symmetrizable Kac-Moody algebras. introduce reduction rule of hom-spaces between Verma modules different algebras which yield some applications on module homomorphisms.
منابع مشابه
Projections of Singular Vectors of Verma Modules over Rank 2 Kac–Moody Lie Algebras
We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac–Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2 (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fuchs and Malikov [Funct. Anal. Appl. 20 (1986), no. 2, 103–113]. In the simpler case of A1 the for...
متن کاملModule homomorphisms from Frechet algebras
We first study some properties of $A$-module homomorphisms $theta:Xrightarrow Y$, where $X$ and $Y$ are Fréchet $A$-modules and $A$ is a unital Fréchet algebra. Then we show that if there exists a continued bisection of the identity for $A$, then $theta$ is automatically continuous under certain condition on $X$. In particular, every homomorphism from $A$ into certain Fr...
متن کاملA Certain Class of Character Module Homomorphisms on Normed Algebras
For two normed algebras $A$ and $B$ with the character space $bigtriangleup(B)neq emptyset$ and a left $B-$module $X,$ a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$ as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...
متن کاملOn Classification of Lorentzian Kac–moody Algebras
We discuss a general theory of Lorentzian Kac–Moody algebras which should be a hyperbolic analogy of the classical theories of finite-dimensional semisimple and affine Kac–Moody algebras. First examples of Lorentzian Kac–Moody algebras were found by Borcherds. We consider general finiteness results about the set of Lorentzian Kac–Moody algebras and the problem of their classification. As an exa...
متن کاملA Theory of Lorentzian Kac–moody Algebras
We present a variant of the Theory of Lorentzian (i. e. with a hyperbolic generalized Cartan matrix) Kac–Moody algebras recently developed by V. A. Gritsenko and the author. It is closely related with and strongly uses results of R. Borcherds. This theory should generalize well-known Theories of finite Kac–Moody algebras (i. e. classical semi-simple Lie algebras corresponding to positive genera...
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 Pure and Applied Algebra
سال: 2022
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2021.106868