On the coalgebra description of OCHA

Hoefel, Eduardo

doi:10.1016/j.jpaa.2011.08.008

Cited by 5 publications

(4 citation statements)

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“…Thus we proved that a codifferentialQ on the coalgebra S(V, A) gives us a Ger ∞ -algebra structure on V , an A ∞ -structure on A, and an L ∞ -morphism from V to the ΛLie-algebra [27] open-closed homotopy algebras (OCHA). These homotopy algebras were studied in papers [23], [24], [28], and [29]. In this subsection we show that the operad Ger + ∞ is a natural extension of the operad OC ∞ .…”

Section: )mentioning

confidence: 90%

“…Inspired by Zwiebach's open-closed string field theory [48] H. Kajiura and J. Stasheff introduced in [27] open-closed homotopy algebras (OCHA). These homotopy algebras were studied in papers [23], [24], [28], and [29]. In this subsection we show that the operad Ger + ∞ is a natural extension of the operad OC ∞ .…”

Section: Ger + ∞ Versus the Operad Oc ∞ Governing Open-closed Homotop...mentioning

confidence: 90%

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Formality Theorem for Hochschild Cochains via Transfer

Dolgushev

2011

Lett Math Phys

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Belatedly to Simon Lyakhovich on the occasion of his 50th birthday. AbstractWe construct a 2-colored operad Ger + ∞ which, on the one hand, extends the operad Ger ∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras (OCHA). We show that Tamarkin's Ger ∞ -structure on the Hochschild cochain complex C • (A, A) of an A ∞algebra A extends naturally to a Ger + ∞ -structure on the pair (C • (A, A), A) . We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this Ger + ∞ -structure to the cohomology of the pair (C • (A, A), A) . We show that Ger + ∞ is a sub DG operad of the first sheet E 1 (SC) of the homology spectral sequence for the Fulton-MacPherson version SC of Voronov's Swiss Cheese operad. Finally, we prove that the DG operads Ger + ∞ and E 1 (SC) are non-formal.

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Section: )mentioning

confidence: 90%

Section: Ger + ∞ Versus the Operad Oc ∞ Governing Open-closed Homotop...mentioning

confidence: 90%

Formality Theorem for Hochschild Cochains via Transfer

Dolgushev

2011

Lett Math Phys

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“…Dennis and I have each dealt with homotopy theory arising from strings. For Dennis, there is his work with Chas [3] which gave rise to a major industry of string topology, whereas in my work with Kajiura [15], [17], [16] and in work of Hoefel [10], [9], there is translation of the physicists string field theory into homotopical algebra. Earlier, I had planned to compare and contrast the various ∞-algebra structures that arise in these different approaches, but I find that there are now established a plethora of such structures and considerable further work in progress, e.g.…”

Section: A String Of Intersectionsmentioning

confidence: 99%

How Dennis and I intersected

Stasheff

2013

Pure and Applied Mathematics Quarterly

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This paper is a slightly modified version of the talk I gave at the Dennisfest. After some reminiscences about how things were in the good old days, including how Dennis' work and mine were somewhat transverse ;-) I will review and update my ancient, unpublished (now arXived) paper with Mike Schlessinger on the deformation theory of rational homotopy types. Then, I will return briefly to another transverse intersection of my work with Dennis'.

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“…Open bosonic string field theory was first formulated as a cubic theory using the (Witten's) associative product [3] but can be extended to that with an A ∞ structure more generally [4,5]. This is also deformed to the theory on general closed string backgrounds [6][7][8] based on the open-closed homotopy algebra (OCHA) structure [9][10][11]. In the superstring field theories, the homotopy algebra structure is more important.…”

Section: Introductionmentioning

confidence: 99%

Open-closed homotopy algebra in superstring field theory

Kunitomo¹

2022

Preprint

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We construct open-closed superstring interactions based on the open-closed homotopy algebra structure. It provides a classical open superstring field theory on general closed-superstringfield backgrounds described by classical solutions of the nonlinear equation of motion of the closed superstring field theory. We also give the corresponding WZW-like action through the map connecting the homotopy-based and WZW-like formulations.4 Open-closed superstring field theory with OCHA-structure 4.

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On the coalgebra description of OCHA

Cited by 5 publications

References 10 publications

Formality Theorem for Hochschild Cochains via Transfer

Formality Theorem for Hochschild Cochains via Transfer

How Dennis and I intersected

Open-closed homotopy algebra in superstring field theory

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