arXiv subjects

Serkan Sütlü

Publications and source records attributed to Serkan Sütlü.

24 records · Page 2Linked to original sources

arXiv2016

Hamiltonian dynamics on matched pairs

It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie-Poisson bracket is derived. As an example, Lie-Poisson equations on $\mathfrak{sl}(2,\mathbb{C})^\ast$ are obtained.

math.DG↗

arXiv2016

Hochschild Cohomology of Reduced Incidence Algebras

We compute the Hochschild cohomology of the reduced incidence algebras such as the algebra of formal power series, the algebra of exponential power series, the algebra of Eulerian power series, and the algebra of formal Dirichlet series. We achieve the result by carrying out the computation on the coalgebra ${\rm Cotor}$-groups of their pre-dual coalgebras. Using the same coalgebraic machinery, we further identify the Hochschild cohomology groups of an incidence algebra associated to a quiver with the ${\rm Ext}$-groups of the incidence algebra associated to a suspension of the quiver.

math.KT↗

arXiv2015

Cyclic homology for Hom-associative algebras

In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.

math.KT↗

arXiv2015

Cyclic Homology and Quantum Orbits

A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with SAYD coefficients is presented. The isomorphism can be viewed as the cyclic-homological counterpart of the Takeuchi-Galois correspondence between the left coideal subalgebras and the quotient right module coalgebras of a Hopf algebra. A spectral sequence generalizing the classical computation of Hochschild homology of a Hopf algebra to the case of arbitrary homogeneous quotient-coalgebra-Galois extensions is constructed. A Pontryagin type self-duality of the Takeuchi-Galois correspondence is combined with the cyclic duality of Connes in order to obtain dual results on the invariant cyclic homology, with SAYD coefficients, of algebras of invariants in homogeneous quotient-coalgebra-Galois extensions. The relation of this dual result with the Chern character, Frobenius reciprocity, and inertia phenomena in the local Langlands program, the Chen-Ruan-Brylinski-Nistor orbifold cohomology and the Clifford theory is discussed.

math.KT↗

arXiv2014

Hopf-cyclic Cohomology of Quantum Enveloping Algebras

In this paper we calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra $U_q(\mathfrak{g})$ for an arbitrary semi-simple Lie algebra $\mathfrak{g}$ with coefficients in a modular pair in involution. We show that its Hochschild cohomology is concentrated in a single degree determined by the rank of the Lie algebra $\mathfrak{g}$.

math.KT↗

arXiv2013

Hopf-cyclic cohomology of bicrossed product Hopf algebras

In this dissertation we study the coefficients spaces (SAYD modules) of Hopf-cyclic cohomology theory over a certain family of bicrossed product Hopf algebras, and we compute the Hopf-cyclic cohomology of such Hopf algebras with coefficients. We associate a Hopf algebra, what we call a Lie-Hopf algebra, to any matched pair of Lie groups, Lie algebras and affine algebraic groups via the semi-dualization procedure of Majid. We then identify the SAYD modules over Lie-Hopf algebras with the representations and corepresentations of the total Lie group, Lie algebra or the affine algebraic group of the matched pair. First we classify the SAYD modules that correspond only to the representations of a total Lie group (algebra). We call them induced SAYD modules. We then generalize this identification, focusing on the matched pair of Lie algebras. We establish a one-to-one correspondence between the SAYD modules over the Lie-Hopf algebra associated to a matched pair of Lie algebras and certain SAYD modules over the total Lie algebra. Once the SAYD modules are associated to the representations and the corepresentations of Lie algebras, nontrivial examples can be constructed. This way, we illustrate a highly nontrivial 4-dimensional SAYD module over the Schwarzian Hopf algebra H_{1S}. In addition, we discuss the periodic cyclic cohomology of Lie-Hopf algebras with nontrivial SAYD coefficients. We obtain a general van Est isomorphism identifying the periodic cyclic cohomology of a Lie-Hopf algebra with the (relative) Lie algebra cohomology of the corresponding total Lie algebra.

math.KT↗