Happel, Dieter,
Triangulated Categories in the Representation of Finite Dimensional Algebras / Dieter Happel. - Cambridge : Cambridge University Press, 1988. - 1 online resource (220 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 119 . - London Mathematical Society Lecture Note Series ; no. 119. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. 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 interated 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.
9780511629228 (ebook)
Categories (Mathematics)
Representations of algebras
Modules (Algebra)
QA169 / .H36 1988
512/.55
Triangulated Categories in the Representation of Finite Dimensional Algebras / Dieter Happel. - Cambridge : Cambridge University Press, 1988. - 1 online resource (220 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 119 . - London Mathematical Society Lecture Note Series ; no. 119. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. 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 interated 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.
9780511629228 (ebook)
Categories (Mathematics)
Representations of algebras
Modules (Algebra)
QA169 / .H36 1988
512/.55