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Stratifying algebras with near-matrix algebras. (English) Zbl 1044.16006

For a left module \(U\) and a right module \(V\) over an algebra \(D\) with a \(D\)-\(D\) bilinear form \(\beta\colon U\times V\to D\), an associative algebra structure can be defined on the tensor product \(V\otimes_DU\) which is called a near matrix algebra. In the present paper, the authors investigate algebras filtered by near matrix algebras and establish a unified treatment of quasi-hereditary algebras, cellular algebras and stratified algebras.

MSC:

16G20 Representations of quivers and partially ordered sets
16P10 Finite rings and finite-dimensional associative algebras
20G05 Representation theory for linear algebraic groups
16S50 Endomorphism rings; matrix rings
16W70 Filtered associative rings; filtrational and graded techniques
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References:

[1] Auslander, M.; Reiten, I.; Smalo, S. O., Representation Theory of Artin Algebras (1997), Cambridge University Press: Cambridge University Press Cambridge
[2] Cline, E.; Parshall, B.; Scott, L., Finite dimensional algebras and highest weight categories, J. Reine Angew. Math., 391, 85-99 (1988) · Zbl 0657.18005
[3] Cline, E.; Parshall, B.; Scott, L., Integral and graded quasi-hereditary algebras, J. Algebra, 131, 126-160 (1990) · Zbl 0699.16015
[4] Cline, E.; Parshall, B.; Scott, L., Stratifying endomorphism algebras, Mem. AMS, 591 (1996) · Zbl 0888.16006
[6] Du, J.; Parshall, B.; Scott, L., Stratifying endomorphism algebras associated to Hecke algebras, J. Algebra, 203, 169-210 (1998) · Zbl 0920.20008
[7] Du, J.; Rui, R., Based algebras and standard bases for quasi-hereditary algebras, Trans. Amer. Math. Soc., 350, 3207-3235 (1998) · Zbl 0908.16015
[8] Graham, J.; Lehrer, G., Cellular algebras, Invent. Math., 123, 1-34 (1996) · Zbl 0853.20029
[9] Wiedemann, A., On stratifications of derived module categories, Canad. Math. Bull., 34, 275-280 (1991) · Zbl 0753.16006
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