GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 241-257
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Classification of AS-regular algebras is one of the major projects in non-commutative algebraic geometry. In this paper, we will study when given AS-regular algebras are graded Morita equivalent. In particular, for every geometric AS-regular algebra A, we define another graded algebra A, and show that if two geometric AS-regular algebras A and A' are graded Morita equivalent, then A and A' are isomorphic as graded algebras. We also show that the converse holds in many three-dimensional cases. As applications, we apply our results to Frobenius Koszul algebras and Beilinson algebras.
MORI, IZURU; UEYAMA, KENTA. GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 241-257. doi: 10.1017/S001708951200047X
@article{10_1017_S001708951200047X,
author = {MORI, IZURU and UEYAMA, KENTA},
title = {GRADED {MORITA} {EQUIVALENCES} {FOR} {GEOMETRIC} {AS-REGULAR} {ALGEBRAS}},
journal = {Glasgow mathematical journal},
pages = {241--257},
year = {2013},
volume = {55},
number = {2},
doi = {10.1017/S001708951200047X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951200047X/}
}
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