Modified Ringel-Hall algebras, naive lattice algebras and lattice algebras

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 671-688
• 页数: 18页
• 语种: 英文

摘要

For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra.Furthermore,the kernel of this epimorphism is described explicitly.Finally,we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories.