Noncommutative geometry and dual coalgebras Export

@article{citeulike:3134573, abstract = {In <a href="/abs/math/0606241v2">arXiv:math/0606241v2</a> M. Kontsevich and Y. Soibelman argue that the category of noncommutative (thin) schemes is equivalent to the category of coalgebras. We propose that under this correspondence the affine scheme of a k-algebra A is the dual coalgebra A^o and draw some consequences. In particular, we describe the dual coalgebra A^o of A in terms of the A-infinity structure on the Yoneda-space of all the simple finite dimensional A-representations.}, archivePrefix = {arXiv}, author = {Le Bruyn, Lieven}, citeulike-article-id = {3134573}, citeulike-linkout-0 = {http://arxiv.org/abs/0805.2377}, citeulike-linkout-1 = {http://arxiv.org/pdf/0805.2377}, day = {15}, eprint = {0805.2377}, keywords = {noncommutative-geometry}, month = {May}, posted-at = {2009-07-16 22:31:55}, priority = {2}, title = {Noncommutative geometry and dual coalgebras}, url = {http://arxiv.org/abs/0805.2377}, year = {2008} }

TY - JOUR ID - citeulike:3134573 L3 - citeulike-article-id:3134573 N2 - In <a href="/abs/math/0606241v2">arXiv:math/0606241v2</a> M. Kontsevich and Y. Soibelman argue that the category of noncommutative (thin) schemes is equivalent to the category of coalgebras. We propose that under this correspondence the affine scheme of a k-algebra A is the dual coalgebra A^o and draw some consequences. In particular, we describe the dual coalgebra A^o of A in terms of the A-infinity structure on the Yoneda-space of all the simple finite dimensional A-representations. TI - Noncommutative geometry and dual coalgebras KW - noncommutative-geometry AU - Le Bruyn, Lieven PY - 2008/May/15/ UR - http://arxiv.org/abs/0805.2377 ER -