Homogeneous algebras

Abstract

Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree 1 with homogeneous relations of degree N. Such algebras are referred to as {\sl homogeneous algebras of degree N}. In particular it is shown that the Koszul complexes of quadratic algebras generalize as N-complexes for homogeneous algebras of degree N.

24 pages

References in corpus (1)

• Tensor fields of mixed Young symmetry type and N-complexes

Cited by in corpus (21)

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• Inhomogeneous Yang-Mills algebras
• Representations of non-commutative quantum groups
• A criterion for homogeneous potentials to be 3-Calabi-Yau
• Tensor product of N-complexes and generalization of graded differential algebras
• Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres
• Automorphisms of Regular Algebras
• Grothendieck-Verdier duality patterns in quantum algebra
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• Multilinear forms and graded algebras
• (a,b)-Koszul algebras
• Calabi-Yau algebras viewed as deformations of Poisson algebras
• Graded algebras and multilinear forms
• Representations of Aut(A(Gamma)) acting on homogeneous components of A(Gamma) and A(Gamma) dual
• Quadratic categories and Koszul resolutions
• From Koszul duality to Poincaré duality
• A duality theorem for generalized Koszul algebras