The present paper mainly considers the representation type of the enveloping algebra of monomial algebra. Let A be a monomial algebra and Aᵉ= A⊗l\!k Aᵒᵖ its enveloping algebra. It is shown that Aᵉ is representation-finite if and only if A Aₙ/rad² Aₙ, where Aₙ is the path algebra l\!kQ with Q = 1 2 ⋯ n. Moreover, we show that the number of all isoclasses of indecomposable (Aₙ/ rad²Aₙ)ᵉ-modules is 4/3n³ + n²-7/3n+1, and classify all indecomposable modules over (Aₙ/ rad²Aₙ)ᵉ. Finally, the Clebsch-Gordon problem over (Aₙ/ rad²Aₙ)ᵉ is studied.
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Zhou et al. (2024) studied this question.
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