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Triangular Decomposition of the Composition Algebra of the Kronecker Algebra

✍ Scribed by Pu Zhang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
201 KB
Volume
184
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let A be a finite-dimensional hereditary algebra over a finite field, and let Ε½ .

Ž . H H A and C C A be, respectively, the Ringel᎐Hall algebra and the composition w x Ž . w x algebra of A. Define r to be the element Ý M g H H A , where M runs over d the isomorphism classes of the regular A-modules with dimension vector d. We Ž . prove that r and the exceptional A-modules all lie in C C A . Let K be the d Ž . Ž . Kronecker algebra, P P resp. I I the subalgebra of C C K generated by the Ž . preprojective resp. preinjective K-modules, and T T the subalgebra generated by Ž . r for n G 0. Then we prove that C C K s P P и T T и I I and then T T is just the Ž n, n.

Ε½ . subalgebra of C C K generated by all regular elements.

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