arXiv subjects

S. Sütlü

Publications and source records attributed to S. Sütlü.

7 recordsLinked to original sources

arXiv2022

Bicocycle Double Cross Constructions

We introduce the notion of a bicocycle double cross product (resp. sum) Lie group (resp. Lie algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a Lie group on the product space of two pointed manifolds, none of which being necessarily a subgroup. On the level of Lie algebras, similarly, a Lie algebra is obtained on the direct sum of two vector spaces, none of which is required to be a subalgebra. Finally, on the quantum level the theory presents a bialgebra, on the tensor product of two (co)algebras that are not necessarily sub-bialgebras, the semidual of which being a cocycle bicrossproduct bialgebra.

math.QA↗

arXiv2021

Cohomologies and generalized derivation extensions of $n$-Lie algebras

A cohomology theory, associated to a $n$-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for $n=3$, with the known cohomology of $n$-Lie algebras. The abelian extensions and infinitesimal deformations of $n$-Lie algebras, on the other hand, are shown to be characterized by the usual cohomology of $n$-Lie algebras. Furthermore, the Hochschild-Serre spectral sequence of the Lie algebra cohomology is upgraded to the level of $n$-Lie algebras, and is applied to the cohomology of generalized derivation extensions.

math.RA↗

arXiv2019

Matched pairs of $m$-invertible Hopf quasigroups

The matched pair theory (of groups) is studied for a class of quasigroups; namely, the $m$-inverse property loops. The theory is upgraded to the Hopf level, and the "$m$-invertible Hopf quasigroups" are introduced.

math.RA↗

arXiv2019

Hom-Lie-Hopf algebras

We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general $(α,β)$-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of $(α,{\rm Id})$-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that, the semi-dualization of a double cross product Hom-Hopf algebra is a bicrossproduct Hom-Hopf algebra. In particular, we apply this result to the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras to obtain Hom-Lie-Hopf algebras.

math.RA↗

arXiv2017

Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients

We discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebra $\mathcal{H}_n$. More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of $\mathcal{H}_n$, and we show that the van Est type characteristic homomorphism from the Hopf-cyclic complex of $\mathcal{H}_n$ to the Gelfand-Fuks cohomology of the Lie algebra $W_n$ of formal vector fields on $\mathbb{R}^n$ respects this multiplicative structure. We then illustrate the machinery for $n=1$.

math.KT↗

arXiv2016

A characteristic map for compact quantum groups

We show that if $G$ is a compact Lie group and $\mathfrak{g}$ is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra $U_q(\mathfrak{g})$ to the twisted cyclic cohomology of quantum group algebra $\mathcal{O}(G_q)$. We also show that the Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podleś sphere $\mathcal{O}(S^2_q)$ is in the image of this map.

math.QA↗

arXiv2015

Hopf-dihedral (co)homology and $L$-theory

We develop an appropriate dihedral extension of the Connes-Moscovici characteristic map for Hopf *-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial $L$-theory classes of a *-algebra that carry a Hopf symmetry over a Hopf *-algebra. Using our machinery we detect a previously unknown $L$-class of the standard Podleś sphere.

math.KT↗