Ringel–Hall algebras of hereditary pure semisimple coalgebras

Kosakowska, Justyna

doi:10.4064/cm115-1-7

Colloq. Math.

2009

DOI: 10.4064/cm115-1-7

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Ringel–Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska

Abstract: Abstract. We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

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“…However, the proof is left to the reader (consult [14,Section 2]). Now we collect the basic properties of the incidence coalgebra K I.…”

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Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

Simson

2009

Colloq. Math.

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Abstract. The incidence coalgebras C = K I of intervally finite posets I and their comodules are studied by means of their Cartan matrices and the Euler integral bilinear form bC :One of our main results asserts that, under a suitable assumption on I, C is an Euler coalgebra with the Euler defect ∂C : I . We also show that, for any poset I of width two, the Grothendieck group K0(K I-Comod fc ) of the category of finitely copresented K I-comodules is generated by the classes [SI (a)] of the simple comodules SI (a) and the classes [EI (a)] of the injective covers EI (a) of SI (a), with a ∈ I.

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“…However, the proof is left to the reader (consult [14,Section 2]). Now we collect the basic properties of the incidence coalgebra K I.…”

mentioning

confidence: 99%

Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

Simson

2009

Colloq. Math.

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Ringel–Hall algebras of hereditary pure semisimple coalgebras

Abstract: Abstract. We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

Cited by 1 publication

References 13 publications

Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

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