Remarks 1 2 Extensions and Categorical Background 2 3 Steinitz - Hall Algebra
نویسنده
چکیده
The general notion of what is now called Hall algebra or Ringel-Hall algebra is an algebra defined out of a certain type of category, a "finitary abelian category". Finitary abelian categories are, roughly speaking, categories where the notions of exact sequences make sense and such that for any pair of objects A,B in the category in question, we have # Hom(A,B) <∞ and # Ext1(A,B) <∞. The Hall algebra of a finitary category encloses informations about isomorphism classes of objects, exentions of objects and so on.
منابع مشابه
ar X iv : m at h / 05 05 14 8 v 1 [ m at h . A G ] 9 M ay 2 00 5 ON THE HALL ALGEBRA OF AN ELLIPTIC CURVE , I
These rings admit numerous algebraic and geometric realizations, but one of the historically first constructions, which dates back to the work of Steinitz in 1900 and later completed by Hall, was given in terms of what is now called the classical Hall algebra H (see [Ma], Chapter III ). This algebra has a basis consisting of isomorphism classes of abelian q-groups, where q is a fixed prime powe...
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These rings admit numerous algebraic and geometric realizations, but one of the historically first constructions, dating to the work of Steinitz in 1900 completed later by Hall, was given in terms of what is now called the classical Hall algebra H (see [Ma], Chapter II ). This algebra has a basis consisting of isomorphism classes of abelian q-groups, where q is a fixed prime power, and the stru...
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