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Triangulated Categories in the Representation of Finite Dimensional Algebras (London Mathematical Society Lecture Note Series)
Rok: 1988
ISBN: 9780521339223
OKCZID: 110076800
Citace (dle ČSN ISO 690):
HAPPEL, Dieter. Triangulated categories in the representation theory of finite dimensional algebras. Cambridge: Cambridge University Press, 1988. ix, 208 s. London Mathematical Society lecture note series, 119.
Anotace
Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite=dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and iterated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.