O anel de GREEN da álgebra de TAFT

Abstract

The aim of this work is to characterize the Green ring of Taft algebra, denoted by 𝑇�𝑁�(𝑞�), where 𝑁� is a positive integer greater than 1 and 𝑞� is a primitive root of unity of order 𝑁�. The Green ring, denoted by 𝑟�(𝑇�𝑁�(𝑞�)), is generated by the isomorphism classes [𝑀�] of finite dimensional 𝑇�𝑁�(𝑞�)-modules with addition given by [𝑀�] + [𝑁�] = [𝑀� ⊕ 𝑁�] and multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms of indecomposable finite dimensional 𝑇�𝑁�(𝑞�)-modules. In this work we describe the indecomposable 𝑇�𝑁�(𝑞�)-modules and the tensorial product between these. From that we show that 𝑟�(𝑇�𝑁�(𝑞�)) is a commutative ring generated by two elements subject to certain relations.