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