On standard derived equivalences of orbit categories

Standard

On standard derived equivalences of orbit categories. / Volkov, Y.; Zvonareva, A.

In: Algebras and Representation Theory, Vol. 21, No. 1, 01.02.2018, p. 195-217.

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

Author

Volkov, Y. ; Zvonareva, A. / On standard derived equivalences of orbit categories. In: Algebras and Representation Theory. 2018 ; Vol. 21, No. 1. pp. 195-217.

BibTeX

@article{1905be9df3d44c959618dffbb860033e,

title = "On standard derived equivalences of orbit categories",

abstract = "Let k be a commutative ring, A and ℬ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ to KpbA, where KpbA is the homotopy category of finitely generated projective A-complexes. We construct a map from the set of standard G-equivalences to the set of standard equivalences from Kpbℬ to KpbA and a map from the set of standard G-equivalences from Kpbℬ to KpbA to the set of standard equivalences from Kpb(ℬ/G) to Kpb(A/G), where A/ G denotes the orbit category. We investigate the properties of these maps and apply our results to the case where A= ℬ= R is a Frobenius k-algebra and G is the cyclic group generated by its Nakayama automorphism ν. We apply this technique to obtain the generating set of the derived Picard group of a Frobenius Nakayama algebra over an algebraically closed field.",

keywords = "Category with group action, Derived Picard group, Derived equivalences, Frobenius algebra, Nakayama algebras, Orbit category, PICARD GROUP, GALOIS COVERING FUNCTORS",

author = "Y. Volkov and A. Zvonareva",

year = "2018",

month = feb,

day = "1",

doi = "10.1007/s10468-017-9710-3",

language = "English",

volume = "21",

pages = "195--217",

journal = "Algebras and Representation Theory",

issn = "1386-923X",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - On standard derived equivalences of orbit categories

AU - Volkov, Y.

AU - Zvonareva, A.

PY - 2018/2/1

Y1 - 2018/2/1

N2 - Let k be a commutative ring, A and ℬ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ to KpbA, where KpbA is the homotopy category of finitely generated projective A-complexes. We construct a map from the set of standard G-equivalences to the set of standard equivalences from Kpbℬ to KpbA and a map from the set of standard G-equivalences from Kpbℬ to KpbA to the set of standard equivalences from Kpb(ℬ/G) to Kpb(A/G), where A/ G denotes the orbit category. We investigate the properties of these maps and apply our results to the case where A= ℬ= R is a Frobenius k-algebra and G is the cyclic group generated by its Nakayama automorphism ν. We apply this technique to obtain the generating set of the derived Picard group of a Frobenius Nakayama algebra over an algebraically closed field.

AB - Let k be a commutative ring, A and ℬ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ to KpbA, where KpbA is the homotopy category of finitely generated projective A-complexes. We construct a map from the set of standard G-equivalences to the set of standard equivalences from Kpbℬ to KpbA and a map from the set of standard G-equivalences from Kpbℬ to KpbA to the set of standard equivalences from Kpb(ℬ/G) to Kpb(A/G), where A/ G denotes the orbit category. We investigate the properties of these maps and apply our results to the case where A= ℬ= R is a Frobenius k-algebra and G is the cyclic group generated by its Nakayama automorphism ν. We apply this technique to obtain the generating set of the derived Picard group of a Frobenius Nakayama algebra over an algebraically closed field.

KW - Category with group action

KW - Derived Picard group

KW - Derived equivalences

KW - Frobenius algebra

KW - Nakayama algebras

KW - Orbit category

KW - PICARD GROUP

KW - GALOIS COVERING FUNCTORS

UR - http://www.scopus.com/inward/record.url?scp=85021727040&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/standard-derived-equivalences-orbit-categories

U2 - 10.1007/s10468-017-9710-3

DO - 10.1007/s10468-017-9710-3

M3 - Article

VL - 21

SP - 195

EP - 217

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 1

ER -

ID: 5808271