We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class.

We introduce a large class of infinite dimensional associative algebras which generalize down-up algebras. Let K be a field and fix f ∈ K[x] and r, s, γ ∈ K. Define L = L(f, r, s, γ ) to be the algebra generated by d, u and h with defining relations:Included in this family are Smith's class of algebras similar to U(sl 2 ), Le Bruyn's conformal sl 2 enveloping algebras and the algebras studied by Rueda. The algebras L have Gelfand-Kirillov dimension 3 and are Noetherian domains if and only if rs = 0. We calculate the global dimension of L and, for rs = 0, classify the simple weight modules for L, including all finite dimensional simple modules. Simple weight modules need not be classical highest weight modules.  2004 Elsevier Inc. All rights reserved.

CiteSeerX-Kazhdan-Lusztig polynomials for hermitian symmetric. was shown for the classical Hermitian symmetric cases that these sets of roots. analyze the categories of highest weight modules with a semiregular general-Highest weight modules, Verma modules, Hermitian symmetric pairs,.. Categories of highest weight modules: Applications to classical Hermitian symmetric. Highest weight modules for Hermitian symmetric pairs of exceptional. Multiplicity-free Theorems of the Restrictions of Unitary Highest. highest weight categories arising from khovanov's diagram algebra i Finite-dimensional algebras and highest weight categories, J. reine angew. Math. 44 T J Enright and B Shelton, Categories of highest weight modules: applications to classical. Hermitian symmetric pairs, Memoirs AMS 67 1987, no. 367. Vitae-Franklin College Faculty-University of Georgia Filtrations on generalized Verma modules for Hermitian symmetric pairs. Categories of highest weight modules: applications to classical Hermitian symmetric Compressed PostScript file-European Mathematical Society The complex analytic methods have found a wide range of applications in the study. of restricting highest weight modules with respect to reductive symmetric pairs. the Plancherel theorem for Hermitian symmetric spaces also for line bundle multiplicity-free representation branching rule symmetric pair highest weight Highest Weight Modules for Hermitian Symmetric Pairs of.-JStor Quasi-hereditary algebras and highest weight categories play an important role in representation. which again comes along with three distinguished classes of modules. Cellular algebras. application of the results about GLmn from Part IV see BS for details Choose a symmetric pair of a cup and a cap in the. Title, Categories of Highest Weight Modules: Applications to Classical Hermitian Symmetric Pairs Volume 367 of American Mathematical Society: Memoirs of the. Bibliography 7 T. J. Enright and B. Shelton, Categories of highest weight modules: applications to classical Hermitian symmetric pairs, to appear in Mem.Amer. Math. Soc. Full Text PDF Publication » Categories of highest weight modules: applications to classical Hermitian symmetric pairs / Thomas J. Enright and Brad Shelton. Multiplicity-free theorems of the restrictions of unitary highest weight. irreducible Hermitian symmetric pair G,K with integral highest weights Categories of highest weight modules: applications to classical Hermitian symmetric Representation Theory of Lie Groups-IMS Highest weight modules for Hermitian symmetric pairs of exceptional type. Categories of highest weight modules: applications to classical Hermitian symmetric For screen-MSP 1987, English, Book, Illustrated edition: Categories of highest weight modules: applications to classical Hermitian symmetric pairs / Thomas J. Enright and Brad Categories of Highest Weight Modules: Applications to Classical. Amazon.co.jp? Categories of Highest Weight Modules: Applications to Classical Hermitian Symmetric Pairs Memoirs of the American Mathematical Society: Boe,...

This work was started as an attempt to apply theory from noncommutative graded algebra to questions about the holonomy algebra of a hyperplane arrangement. We soon realized that these algebras and their deformations, which form a class of quadratic graded algebras, have not been studied much and yet are interesting to algebra, arrangement theory and combinatorics.

It is proved that there exists a scheme that represents the functor of line modules over a graded algebra, and it is called the line scheme of the algebra. Its properties and its relationship to the point scheme are studied. If the line scheme of a quadratic, Auslander-regular algebra of global dimension 4 has dimension 1, then it determines the defining relations of the algebra.Moreover, the following counter-intuitive result is proved. If the zero locus of the defining relations of a quadratic (not necessarily regular) algebra on four generators with six defining relations is finite, then it determines the defining relations of the algebra. Although this result is non-commutative in nature, its proof uses only commutative theory.The structure of the line scheme and the point scheme of a 4-dimensional regular algebra is also used to determine basic incidence relations between line modules and point modules. IntroductionNon-commutative algebraic geometry was introduced in the late 1980s by Artin, Tate and Van den Bergh as a tool for classifying and understanding certain noncommutative algebras [3,4]. Roughly speaking, Artin, Tate and Van den Bergh used the category of graded modules over a non-commutative algebra as the space in which to do geometry, the geometric objects being certain graded modules, linear modules, that play the role of linear objects (points, lines, and so forth).This geometric theory has been most successful in the analysis of algebras that are 'deformations' in some sense of polynomial rings. One such class of algebras consists of Artin-Schelter regular algebras that are graded algebras with the same good growth and homological properties as polynomial rings [2]. The theory is also applicable to other types of algebra [27, Chapter 2]. An attractive feature of the theory is that it recovers commutative algebro-geometric results in addition to producing new results for non-commutative algebras.Throughout this paper, k denotes an algebraically closed field such that char(k) = 2. Let B denote a noetherian, positively graded, connected k-algebra generated by homogeneous elements of degree 1. We write gr-B for the category of finitely generated, graded B-modules. Definition 0.1 [1]. Define Proj B to be the triple ((gr-B)/T, O, σ), where T denotes the subcategory of gr-B of torsion modules, O denotes an object of (gr-B)/T that is represented by the right module B, and σ is the operation M −→ M[1] on (gr-B)/T induced by the shift of degree on a B-module. A quantum P 2 , or quantum projective plane, is Proj B, where B is a quadratic Artin-Schelter regular algebra of global dimension 3.