BRST operator for quantum Lie algebras and differential calculus on quantum groups [PDF]
20 pages, LaTeX, Lecture given at the Workshop on "Classical and Quantum Integrable Systems", 8 - 11 January, Protvino, Russia; corrected some typosFor a Hopf algebra A, we define the structures of differential complexes on two dual exterior Hopf ...
Isaev, A. P., Ogievetsky, O. V.
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Quantization of infinitesimal braidings and pre‐Cartier quasi‐bialgebras
Abstract In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre‐Cartier quasi‐bialgebra, which extends the well‐known notion of quasi‐triangular quasi‐bialgebra given by Drinfeld.
Chiara Esposito +3 more
wiley +1 more source
On the topological ranks of Banach ∗$^*$‐algebras associated with groups of subexponential growth
Abstract Let G$G$ be a group of subexponential growth and C→qG$\mathcal C\overset{q}{\rightarrow }G$ a Fell bundle. We show that any Banach ∗$^*$‐algebra that sits between the associated ℓ1$\ell ^1$‐algebra ℓ1(G|C)$\ell ^1(G\,\vert \,\mathcal C)$ and its C∗$C^*$‐envelope has the same topological stable rank and real rank as ℓ1(G|C)$\ell ^1(G\,\vert ...
Felipe I. Flores
wiley +1 more source
A Three‐Stage Causal Root‐Cause Diagnostic Protocol for Nonstationary Industrial Time Series Data
Predictive maintenance (PdM) systems effectively forecast failures, but they often fail to find root causes, particularly when system dynamics change over time. This limitation arises from applying static causal models or decoupled segmentation to handle nonstationary industrial time series. For regime‐aware causal diagnostics and interventional effect
Cansu Yalim +3 more
wiley +1 more source
Cohomology of Lie superalgebras and of their generalizations [PDF]
The cohomology groups of Lie superalgebras and, more generally, of #epsilon# Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial.
Bonn Univ. (Germany). Physikalisches Inst. +2 more
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Matrix Freedman Inequality for Sub‐Weibull Martingales
ABSTRACT In this paper, we establish a matrix Freedman inequality for martingales with sub‐Weibull tails. Under conditional ψα$$ {\psi}_{\alpha } $$ control of the increments, the top eigenvalue admits a non‐asymptotic tail bound with explicit, dimension‐aware constants.
Íñigo Torres
wiley +1 more source
Vertex algebras associated with the representations of the N=1 super Heisenberg-Virasoro and Schrödinger-Virasoro algebras [PDF]
U ovom radu proučavali smo teoriju reprezentacija dviju važnih generalizacija Heisenberg-Virasorove Liejeve algebre \(\mathcal{H}\), a to su N = 1 super Heisenberg-Virasorova Liejeva algebra \(\mathcal{SH}\) i Schrödinger-Virasorova Liejeva algebra ...
Jandrić, Berislav
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GL‐algebras in positive characteristic II: The polynomial ring
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
Real models for the framed little n$n$‐disks operads
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
The MacMahon Master Theorem for right quantum $\hat gl(m|n)$ [PDF]
International audienceWe prove an analogue of the MacMahon Master Theorem for the right quantumsuperalgebras. In particular, we obtain a new and simple proof of this theoremfor the right quantum algebras.
Ragoucy, E., Molev, A.
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