Results 51 to 60 of about 6,340 (111)
Structure theorems for braided Hopf algebras
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley +1 more source
Operads and moduli spaces of genus $0$ Riemann surfaces
, 1994 We study a pair of dual operads which arise in the study of moduli spaces of pointed genus 0 curves (this duality is similar to that between commutative and Lie algebras).
Getzler, Ezra
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Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley +1 more source
Locally constant $n$-operads as higher braided operads
Journal of Noncommutative Geometry, 2010 We introduce a category of locally constant n -operads which can be considered as the category of higher braided operads. For
openaire +5 more sources
Homotopical commutative rings and bispans
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We prove that commutative semirings in a cartesian closed presentable ∞$\infty$‐category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product‐preserving functors from the (2,1)‐category of bispans of finite sets. In other words, we identify the latter as the Lawvere theory for commutative semirings in the ∞$\infty$‐categorical
Bastiaan Cnossen +3 more
wiley +1 more source
On several varieties of cacti and their relations
, 2005 Motivated by string topology and the arc operad, we introduce the notion of quasi-operads and consider four (quasi)-operads which are different varieties of the operad of cacti.
Kassel, Penner, Ralph M Kaufmann
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The Mumford conjecture (after Bianchi)
Journal of Topology, Volume 18, Issue 1, March 2025.Abstract We give a self‐contained and streamlined rendition of Andrea Bianchi's recent proof of the Mumford conjecture using moduli spaces of branched covers.
Ronno Das, Dan Petersen
wiley +1 more source
Communications in Algebra, 2005 In this paper, we introduce Adem-Cartan operads and prove that the cohomology of any algebra over such an operad is an unstable level algebra over the extended Steenrod algebra. Moreover we prove that this cohomology is endowed with secondary cohomological operations.
Chataur, D., Livernet, M.
openaire +2 more sources
Operadic comodules and (co)homology theories [PDF]
, 2014 An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a $\mathcal{P ...
Griffin, James
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