Cohomology in algebra, geometry, physicsand statistics

Combinatorics of multilinear differential operators, or still another explanation of the ubiquity of Lie and strongly homotopy Lie algebras

Speaker’s name:

Martin Markl

Speaker’s affiliation:

Institute of Mathematics of the Czech Academy of Sciences

Place:

in IM building, ground floor +ZOOM meeting

Date:

Wednesday, 13. April 2022 - 13:30 to 14:30

Abstract:

As a motivation, we start with an analysis of the interplay between the classical Jacobi identity and differential operators, and

compare it with the effect of the associator. Moving to the `quantized' level, we compare the nature of the big bracket and

IBL(=infinitesimal Lie bialgebras)-infinity algebras with Terilla's quantization of associative algebras.

In the second part, we introduce a filtration mimicking combinatorial properties of multidifferential operators, and

the associated notion of tight operads. We then come back to Lie algebras and give another reason why they deserve

to be, along with commutative and associative algebras, recognized as one of the Three Graces.

The talk will be based on the paper "Calculus of multilinear differential operators, operator $L_\infty$-algebras and $IBL_\infty$-algebras"

of Denis Bashkirov and mine. Its preprint is available at

https://arxiv.org/abs/2108.12158, published version at https://users.math.cas.cz/~markl/.

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We open the blue lecture room at 13.15 for coffee and close it at 15.00

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois

compare it with the effect of the associator. Moving to the `quantized' level, we compare the nature of the big bracket and

IBL(=infinitesimal Lie bialgebras)-infinity algebras with Terilla's quantization of associative algebras.

In the second part, we introduce a filtration mimicking combinatorial properties of multidifferential operators, and

the associated notion of tight operads. We then come back to Lie algebras and give another reason why they deserve

to be, along with commutative and associative algebras, recognized as one of the Three Graces.

The talk will be based on the paper "Calculus of multilinear differential operators, operator $L_\infty$-algebras and $IBL_\infty$-algebras"

of Denis Bashkirov and mine. Its preprint is available at

https://arxiv.org/abs/2108.12158, published version at https://users.math.cas.cz/~markl/.

---------------------------------------------------------------------------------------------------------------------------------------------------

We open the blue lecture room at 13.15 for coffee and close it at 15.00

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

Meeting ID: 995 9841 3922

Passcode: Galois