On the computation of intersection numbers for twisted cocycles

Twisted cocycles of Lie algebras and corresponding invariant functions

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint representation - so called $(α,β,γ)$--derivations. Parametric sets of spaces of cocycles allow us to define complex functions which are invariant under Lie isomorphisms. Such complex functions thus represent useful invariants - we show how they classify three and four-dimensional Lie algebras as well as how they apply to some eight-dimensional one-parametric nilpotent co…

Twisted entire cyclic cohomology, J-L-O cocycles and equivariant spectral triples

We study the "quantized calculus" corresponding to the algebraic ideas related to "twisted cyclic cohomology" introduced in [KMT]. With very similar definitions and techniques as those used in [jlo], we define and study "twisted entire cyclic cohomology" and the "twisted Chern character" associated with an appropriate operator-theoretic data called "twisted spectral data", which consists of a spectral triple in the conventional sense of noncommutative geometry ([Con]) and an additional positive operator having specified properties. Furthermore, it is shown that given a spectral triple (in the …

Twisted Quantum Double Model of Topological Phases in Two--Dimension

We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $α$ over $G$. The detailed properties of the ground states are studied, and we find that the ground--state subspace can be characterized in terms of the twisted quantum double $D^α(G)$ of $G$. When $α$ is the trivial 3-cocycle, the model becomes Kitaev's quantum double model based on the finite group $G$, in which the elementary excitations are known to be classified by the quantum double $D(G)$ of $G$. Our model can be viewed as a Hamiltonian extension of t…

Twisted sigma-model solitons on the quantum projective line

On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional, and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather complicate, the use of the positivity and the bound by the topological term leads to self-duality equations (thus yielding twisted noncommutative sigma-model soliton…

带表示的 Hom-Lie-Yamaguti 代数上由 (2,3)-上循环扭变的 $\mathcal{O}$-算子

Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations

本文在 Hom-Lie-Yamaguti 代数上引入扭变 $\mathcal{O}$-算子，证明其诱导 Hom-Lie-Yamaguti 结构，定义其上同调，并研究其底层 Hom-NS-Lie-Yamaguti 代数及由 Hom-Lie 代数诱导的情形。

面积保持微分同胚环的中心扩张及其模糊球极限

Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits

研究面积保持微分同胚环的中心扩张，并揭示其在大k极限下的模糊球极限性质。