Triangular Decomposition of the Composition Algebra of the Kronecker Algebra
作者： Pu Zhang
关键词: Mathematics 、 Subalgebra 、 Filtered algebra 、 Cellular algebra 、 Symmetric algebra 、 Cartan subalgebra 、 Quaternion algebra 、 Combinatorics 、 Algebra 、 Division algebra 、 Triangular matrix
摘要: Abstract LetAbe a finite-dimensional hereditary algebra over finite field, and let H (A) C be, respectively, the Ringel–Hall composition ofA. Definerdto be element ∑[M]∈ (A), where [M] runs isomorphism classes of regularA-modules with dimension vectord. We prove thatrdand exceptionalA-modules all lie in (A). LetKbe Kronecker algebra, P (resp. I ) subalgebra (K) generated by preprojective preinjective)K-modules, T byr(n, n)forn≥0. Then we that (K)= · then is just regular elements.
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sci-hub.se 参考文章(6)
Claus Michael Ringel, Hall algebras revisited ,(1992)
Claus Michael Ringel, PBW-bases of quantum groups. Crelle's Journal. ,vol. 470, pp. 51- 88 ,(1996)
Claus Michael Ringel, From representations of quivers via Hall and Loewy algebras to quantum groups Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Malcev ; 2: Mezdunarodnaja Konferencija po Algebre,1, 1989, Novosibirsk. ,vol. 131, ,(1992)
James A. Green, Hall algebras, hereditary algebras and quantum groups. Inventiones Mathematicae. ,vol. 120, pp. 361- 377 ,(1995) , 10.1007/BF01241133
Claus Michael Ringel, Hall algebras and quantum groups Inventiones Mathematicae. ,vol. 101, pp. 583- 591 ,(1990) , 10.1007/BF01231516
Claus Michael Ringel, The Composition Algebra of a Cyclic Quiver Proceedings of the London Mathematical Society. ,vol. s3-66, pp. 507- 537 ,(1993) , 10.1112/PLMS/S3-66.3.507