Results 71 to 80 of about 34,345 (209)

Cup Coproducts in Hopf Cyclic Cohomology

, 2013
We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group homology ...
Hassanzadeh, Mohammad, Khalkhali, Masoud
core   +1 more source

Model category structures on truncated multicomplexes for complex geometry

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4163-4177, December 2025.
Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to N$N$‐multicomplexes. We present a family of model category structures on the category of N$N$‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism ...
Joana Cirici, Muriel Livernet, Sarah Whitehouse   +2 more
wiley   +1 more source

W‐algebras, Gaussian free fields, and g$\mathfrak {g}$‐Dotsenko–Fateev integrals

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract Based on the intrinsic connection between Gaussian free fields and the Heisenberg vertex algebra, we study some aspects of the correspondence between probability theory and W$W$‐algebras. This is first achieved by providing a construction of the W$W$‐algebra associated to a complex simple Lie algebra g$\mathfrak {g}$ by means of Gaussian free ...
Baptiste Cerclé
wiley   +1 more source

Zhukovsky-Volterra top and quantisation ideals

Nuclear Physics B
In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics—the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson ...
A. Mikhailov, T. Skrypnyk
doaj   +1 more source

Universal Poisson Envelope for Binary-Lie Algebras

Communications in Algebra, 2013
In this article the universal Poisson enveloping algebra for a binary-Lie algebra is constructed. Taking a basis 𝔹 of a binary-Lie algebra B, we consider the symmetric algebra S(B) of polynomials in the elements of 𝔹. We consider two products in S(B), the usual product of polynomials fg and the braces {f, g}, defined by the product in B
Arenas, Manuel, Arenas Carmona, Luis
openaire   +4 more sources

GL‐algebras in positive characteristic II: The polynomial ring

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley   +1 more source

Finite W-algebras [PDF]

, 2010
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras.
Losev, Ivan
core  

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source

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

Tau-functions beyond the group elements

Nuclear Physics B
Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a group element, i.e. satisfying the property Δ(X)=X⊗X, then their generating functions obey bilinear Hirota equations and hence are named ...
A. Mironov, V. Mishnyakov, A. Morozov
doaj   +1 more source