Pointed Brauer trees

Mary Schaps; Evelyne Zakay-Illouz

doi:10.1006/jabr.2001.8928

Pointed Brauer trees

Mary Schaps, Evelyne Zakay-Illouz

Department of Mathematics

The Jordan Valley College

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this paper we establish a one-to-one correspondence between Brauer trees with an additional structure that we call "pointing" and equivalence classes of tilting complexes of the corresponding Brauer star algebra which are of a special "combinatorial" nature. Under the correspondence, the identification of the indecomposable summands of the tilting complex with edges of the Brauer tree is completely natural. The procedure gives an algorithm for producing large numbers of distinct tilting complexes for the same Brauer tree.

Original language	English
Pages (from-to)	647-672
Number of pages	26
Journal	Journal of Algebra
Volume	246
Issue number	2
DOIs	https://doi.org/10.1006/jabr.2001.8928
State	Published - 15 Dec 2001

Bibliographical note

Funding Information:
1This work was done for a doctoral dissertation at Bar-Ilan University and was partially supported by the Bar-Ilan Research Authority.

Funding

1This work was done for a doctoral dissertation at Bar-Ilan University and was partially supported by the Bar-Ilan Research Authority.

Funders	Funder number
Bar-Ilan Research Authority

Keywords

Brauer tree
Cyclic detect
Derived equivalent
Tilting complex

Access to Document

10.1006/jabr.2001.8928

Cite this

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N2 - In this paper we establish a one-to-one correspondence between Brauer trees with an additional structure that we call "pointing" and equivalence classes of tilting complexes of the corresponding Brauer star algebra which are of a special "combinatorial" nature. Under the correspondence, the identification of the indecomposable summands of the tilting complex with edges of the Brauer tree is completely natural. The procedure gives an algorithm for producing large numbers of distinct tilting complexes for the same Brauer tree.

AB - In this paper we establish a one-to-one correspondence between Brauer trees with an additional structure that we call "pointing" and equivalence classes of tilting complexes of the corresponding Brauer star algebra which are of a special "combinatorial" nature. Under the correspondence, the identification of the indecomposable summands of the tilting complex with edges of the Brauer tree is completely natural. The procedure gives an algorithm for producing large numbers of distinct tilting complexes for the same Brauer tree.

KW - Brauer tree

KW - Cyclic detect

KW - Derived equivalent

KW - Tilting complex

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ER -

Pointed Brauer trees

Abstract

Bibliographical note

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Keywords

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