@article{Lin2024, 
author = {Shiyu Lin and Shilin Yang},
title = {A new family of positively based algebras                      H              n},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {2602-2618},
keywords = {positively based algebra, indecomposable module, cell module},
url = {https://www.sciopen.com/article/10.3934/math.2024128},
doi = {10.3934/math.2024128},
abstract = {In this paper, we introduce a new family of algebras                      H              n  , which are generated by three generators    x  ,  y  ,  z, with the following relations: (1)        x          2      n        =  1  ,        y    2    =  x  y  +  y  ,    x  y  =  y  x  ; and (2)         z    2    =  z  ,    x  z  =  z  x  =  z  ,    z  y  =  2  z  . First, it shows that                      H              n   is a positively based algebra. Then, all the indecomposable modules of                      H              n   are constructed. Additionally, it shows that the dimension of each indecomposable                      H              n  -module is at most    2. Finally, all the left (right) cells and left (right) cell modules of                      H              n   are described, and the decompositions of the decomposable left cell modules are also obtained.}
}