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Linear Modules over Sklyanin Algebras
Author(s) -
Staniszkis Joanna M.
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/53.3.464
Subject(s) - bijection , mathematics , rank (graph theory) , construct (python library) , pure mathematics , linear algebra , point (geometry) , linear map , algebra over a field , discrete mathematics , combinatorics , computer science , geometry , programming language
Let A = A n ( E , τ) be the n ‐dimensional Sklyanin algebra associated with a smooth elliptic curve E and point τ ∈ E . This paper classifies linear modules over A . We show that d ‐linear modules are in bijection with those d ‐planes in P( A 1 * ) which are either secant to E or are singular loci of certain rank ( n — d — 1)‐quadrics containing E . Moreover, linear modules are Cohen‐Macaulay and critical, and non‐isomorphic linear modules give non‐isomorphic linear spaces in Proj A . We also construct all short exact sequences of linear modules.