منابع مشابه
Some homological algebra
1.1 Adjoint functors Let C and D be categories and let f∗ : C → D and f∗ : D → C be functors. Then f∗ is a right adjoint to f∗ and f∗ is a left adjoint to f∗ if, for each D ∈ D and C ∈ C there is a natural vector space isomorphism HomC(fD,C) Φ −→HomD(D, f∗C). For C ∈ C and D ∈ D define τC = Φ(idf∗C) ∈ HomC(ff∗C,C) and φD = Φ(idf∗D) ∈ HomD(D, f∗fD). In general τC and φD are neither injective nor...
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In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig’s a-function is formulated (and proved for type A). The second part deals with the extension algebra of Verma modules. I...
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In this paper, we are mainly concerned with the Cartan determinant conjecture and the no loop conjecture. If A is an artin algebra of finite global dimension, the first conjecture claims that the Cartan determinant of A is equal to 1, while the second one states that every simple A-module admits only the trivial self-extension. Among numerous partial solutions to these conjectures such as those...
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We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Another consequence is a rather unusual summation formulae in which one side is an infinite basic-hyper...
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We present a formula for the norm of an elementary operator on a C∗-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems not to have been studied previously and has interesting properties. In addition, we characterise compactness of elementary operators. We consider an elementar...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1968
ISSN: 0021-8693
DOI: 10.1016/0021-8693(68)90021-5