Some properties for almost cellular algebras

Yongjie Wang; Nan Gao; Yongjie Wang; Nan Gao

doi:10.3934/era.2020086

Electronic Research Archive

2021, Volume 29, Issue 1: 1681-1689. doi: 10.3934/era.2020086

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Some properties for almost cellular algebras

Yongjie Wang ^{1
,},
Nan Gao ^{2
,
,}

1.
School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China
2.
Department of Mathematics, Shanghai University, Shanghai 200444, China

Received: 01 April 2020 Revised: 01 June 2020 Published: 24 August 2020
16W70, 20C08

In this paper, we will investigate some properties for almost cellular algebras. We compare the almost cellular algebras with quasi-hereditary algebras, which are known to carry any homological and categorical structures. We prove that any almost cellular algebra is the iterated inflation and obtain some sufficient and necessary conditions for an almost cellular algebra $ \mathrm{A} $ to be quasi-hereditary.
- Cellular algebra,
- quasi-hereditary algebra,
- iterated inflations,
- involution,
- filtration
Citation: Yongjie Wang, Nan Gao. Some properties for almost cellular algebras[J]. Electronic Research Archive, 2021, 29(1): 1681-1689. doi: 10.3934/era.2020086

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Abstract

In this paper, we will investigate some properties for almost cellular algebras. We compare the almost cellular algebras with quasi-hereditary algebras, which are known to carry any homological and categorical structures. We prove that any almost cellular algebra is the iterated inflation and obtain some sufficient and necessary conditions for an almost cellular algebra $ \mathrm{A} $ to be quasi-hereditary.

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