Yang-Mills algebra Export

@article{citeulike:884598, abstract = {Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang-Mills connection over the (s+1)-dimensional pseudo Euclidean space are pointed out. This algebra is Gorenstein and Koszul of global dimension 3 but except for s=1 (i.e. in the 2-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Artin-Schelter regular algebra, it fails to be regular in that it has exponential growth. We give an explicit formula for the Poincare series of this algebra A and for the dimension in degree n of the graded Lie algebra of which A is the universal enveloping algebra. In the 4-dimensional (i.e. s=3) Euclidean case, a quotient of this algebra is the quadratic algebra generated by the covariant derivatives of a generic (anti) self-dual connection. This latter algebra is Koszul of global dimension 2 but is not Gorenstein and has exponential growth. It is the universal enveloping algebra of the graded Lie-algebra which is the semi-direct product of the free Lie algebra with three generators of degree one by a derivation of degree one.}, archivePrefix = {arXiv}, author = {Connes, Alain and Dubois-Violette, Michel}, citeulike-article-id = {884598}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0206205}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0206205}, day = {10}, eprint = {math/0206205}, keywords = {yang-mills\_algebra}, month = {Sep}, posted-at = {2009-09-16 10:28:04}, priority = {2}, title = {Yang-Mills algebra}, url = {http://arxiv.org/abs/math/0206205}, year = {2002} }

TY - JOUR ID - citeulike:884598 L3 - citeulike-article-id:884598 N2 - Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang-Mills connection over the (s+1)-dimensional pseudo Euclidean space are pointed out. This algebra is Gorenstein and Koszul of global dimension 3 but except for s=1 (i.e. in the 2-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Artin-Schelter regular algebra, it fails to be regular in that it has exponential growth. We give an explicit formula for the Poincare series of this algebra A and for the dimension in degree n of the graded Lie algebra of which A is the universal enveloping algebra. In the 4-dimensional (i.e. s=3) Euclidean case, a quotient of this algebra is the quadratic algebra generated by the covariant derivatives of a generic (anti) self-dual connection. This latter algebra is Koszul of global dimension 2 but is not Gorenstein and has exponential growth. It is the universal enveloping algebra of the graded Lie-algebra which is the semi-direct product of the free Lie algebra with three generators of degree one by a derivation of degree one. TI - Yang-Mills algebra KW - yang-mills_algebra AU - Connes, Alain AU - Dubois-Violette, Michel PY - 2002/Sep/10/ UR - http://arxiv.org/abs/math/0206205 ER -