Split bounded extension algebras and Han’s
conjecture

Cibils, Claude; Lanzilotta, Marcelo; Marcos, Eduardo N.; Solotar, Andréa

doi:10.2140/pjm.2020.307.63

Cited by 9 publications

(24 citation statements)

References 28 publications

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“…In other words considering

S

with its

B

‐bimodule structure obtained by transport of structure, with ‘zero internal product’ and with ‘zero action on

X

’ provides the same complex

G_{p} / G_{p - 1}

. This complex has been considered in the proof of [7; 9, Proposition 3.3], where we proved that if

{sans-serifTor}_{*}^{B} false(S, S^{\otimes_{B} n} false) = 0

for

* > 0

and for all

n

then for

q > 0

we have

H_{q} false(G_{p} / G_{p - 1} false) = {sans-serifTor}_{p + q}^{B^{e}} false(X, S^{\otimes_{B} p} false)

while

H_{0} false(G_{p} / G_{p - 1} false) = 0

. This finishes the proof in degrees at least

2

since the

B

‐bimodules

S

and

A / B

are isomorphic; see Remark 5.3.…”

Section: Gap Of the Jacobi–zariski Long Nearly Exact Sequencementioning

confidence: 91%

“…The index of nilpotency of M is the smallest n such that M ⊗Λn = 0. Definition 6.4 [7]. Let Λ be a k-algebra and let M be a Λ-bimodule.…”

Section: • • •mentioning

confidence: 99%

“…The category of

A

‐modules is exact with respect to short exact sequences of

A

‐modules which are split as sequences of

B

‐modules; see [3, 23]. The relative projective

A

‐modules are described for instance in [7], they are

A

‐direct summands of induced modules from

B

. A relative projective resolution of an

A

‐module is made with relative projectives and has a

B

‐contracting homotopy; see [15, p. 250].…”

Section: Normalised Relative Bar Resolutionmentioning

confidence: 99%

“…Proof We outline the main steps and tools of the proof. The bimodules involved are induced bimodules, hence they are relative projective; see for instance [7]. A somehow intricate but straightforward computation shows that

d

is well defined with respect to tensor products over

B

.…”

Section: Normalised Relative Bar Resolutionmentioning

confidence: 99%

“…In the last section, as mentioned, we retrieve previous results from [17,18] and we improve the Jacobi-Zariski sequence from [7].…”

Section: Introductionmentioning

confidence: 99%

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Jacobi–Zariski long nearly exact sequences for associative algebras

Cibils

Lanzilotta

Marcos

et al. 2021

Bulletin of London Math Soc

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show abstract

“…In other words considering

S

with its

B

‐bimodule structure obtained by transport of structure, with ‘zero internal product’ and with ‘zero action on

X

’ provides the same complex

G_{p} / G_{p - 1}

. This complex has been considered in the proof of [7; 9, Proposition 3.3], where we proved that if

{sans-serifTor}_{*}^{B} false(S, S^{\otimes_{B} n} false) = 0

for

* > 0

and for all

n

then for

q > 0

we have

H_{q} false(G_{p} / G_{p - 1} false) = {sans-serifTor}_{p + q}^{B^{e}} false(X, S^{\otimes_{B} p} false)

while

H_{0} false(G_{p} / G_{p - 1} false) = 0

. This finishes the proof in degrees at least

2

since the

B

‐bimodules

S

and

A / B

are isomorphic; see Remark 5.3.…”

Section: Gap Of the Jacobi–zariski Long Nearly Exact Sequencementioning

confidence: 91%

“…The index of nilpotency of M is the smallest n such that M ⊗Λn = 0. Definition 6.4 [7]. Let Λ be a k-algebra and let M be a Λ-bimodule.…”

Section: • • •mentioning

confidence: 99%

“…The category of

A

‐modules is exact with respect to short exact sequences of

A

‐modules which are split as sequences of

B

‐modules; see [3, 23]. The relative projective

A

‐modules are described for instance in [7], they are

A

‐direct summands of induced modules from

B

. A relative projective resolution of an

A

‐module is made with relative projectives and has a

B

‐contracting homotopy; see [15, p. 250].…”

Section: Normalised Relative Bar Resolutionmentioning

confidence: 99%

d

is well defined with respect to tensor products over

B

.…”

Section: Normalised Relative Bar Resolutionmentioning

confidence: 99%

“…In the last section, as mentioned, we retrieve previous results from [17,18] and we improve the Jacobi-Zariski sequence from [7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Jacobi–Zariski long nearly exact sequences for associative algebras

Cibils

Lanzilotta

Marcos

et al. 2021

Bulletin of London Math Soc

Self Cite

View full text Add to dashboard Cite

show abstract

Han's conjecture for bounded extensions

Cibils¹,

Lanzilotta

Marcos

et al. 2022

Journal of Algebra

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Strongly stratifying ideals, Morita contexts and Hochschild homology

Cibils,

Lanzilotta,

Marcos

et al. 2024

Journal of Algebra

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Split bounded extension algebras and Han’s conjecture

Abstract: A main purpose of this paper is to prove that the class of finite dimensional algebras which verify Han's conjecture is closed under split bounded extensions.

Cited by 9 publications

References 28 publications

Jacobi–Zariski long nearly exact sequences for associative algebras

Jacobi–Zariski long nearly exact sequences for associative algebras

Han's conjecture for bounded extensions

Strongly stratifying ideals, Morita contexts and Hochschild homology

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