000			03527nam a22004098i 4500
001			CR9781139107105
003			UkCbUP
005			20200124160238.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110706s2009||||enk o ||1 0|eng|d
020			_a9781139107105 (ebook)
020			_z9780521757683 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA200 _b.B38 2009
082	0	0	_a512/.57 _222
100	1		_aBautista, R., _d1943- _eauthor.
245	1	0	_aDifferential tensor algebras and their module categories / _cR. Bautista, L. Salmerón, and R. Zuazua.
246	3		_aDifferential Tensor Algebras & their Module Categories
264		1	_aCambridge : _bCambridge University Press, _c2009.
300			_a1 online resource (ix, 452 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v362
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aT-algebras and differentials -- Dutalgebras and modules -- Bocses, ditalgebras and modules -- Layered ditalgebras -- Exact structures in A-mod -- Quotient ditalgebras -- Frames and roiter ditalgebras -- Product of ditalgebras -- Hom-tensor relations and dual basis -- Admissible modules -- Complete admissible modules -- Bimodule filtrations and triangular admissible modules -- Free bimodule filtrations and free datalgebras -- Examples and applications -- Passage from ditalgebras to finite-dimensional algebras -- Scalar extension and ditalgebras -- Bimodules -- Parametrizing bimodules and wildness -- Nested and seminested ditalgebras -- Critical diatalgebras -- Critical ditalgebras -- Reduction functors -- Reduction functions -- Modules over non-wild ditalgebras -- Tameness and wildness -- Modules over non-wild ditalgebras revisited -- Modules over non-wild algebras -- Absolute wildness -- Generic modules and tameness -- Varieties of modules over ditalgebras -- Ditalgebras of partially ordered sets -- Further examples of wild ditalgebras -- Answers to selected exercises.
520			_aThis volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book.
650		0	_aTensor algebra.
650		0	_aRepresentations of algebras.
650		0	_aCategories (Mathematics)
700	1		_aSalmerón, L., _eauthor.
700	1		_aZuazua, R., _eauthor.
776	0	8	_iPrint version: _z9780521757683
830		0	_aLondon Mathematical Society lecture note series ; _v362.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139107105
999			_c518291 _d518289