# A. A. Kalyuzhnyi

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### On Fourier algebra of a hypergroup constructed from a conditional expectation on a locally compact group

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

Methods Funct. Anal. Topology **23** (2017), no. 1, 37-50

We prove that the Fourier space of a hypergroup constructed from a conditional expectation on a locally compact group has a Banach algebra structure.

### On Fourier algebra of a locally compact hypergroup

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

Methods Funct. Anal. Topology **21** (2015), no. 3, 246-255

We give sufficient conditions for the Fourier and the Fourier-Stieltjes spaces of a locally compact hypergroup to be Banach algebras.

### On infinitesimal structure of a hypergroup that originates from a Lie group

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

Methods Funct. Anal. Topology **17** (2011), no. 4, 319-329

We describe an infinitesimal algebra to a hypergroup constructed from a Lie group and a conditional expectation. We also prove a theorem on a decomposition of the conditional expectation into the product of a counital conditional expectation and the one that arises in the double coset construction.

### Harmonic analysis on a locally compact hypergroup

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

Methods Funct. Anal. Topology **16** (2010), no. 4, 304-332

We propose a new axiomatics for a locally compact hypergroup. On the one hand, the new object generalizes a DJS-hypergroup and, on the other hand, it allows to obtain results similar to those for a unimodular hypecomplex system with continuous basis. We construct a harmonic analysis and, for a commutative locally compact hypergroup, give an analogue of the Pontryagin duality theorem.

### Permutations in tensor products of factors, and $L^{2}$ cohomology of configuration spaces

Alexei Daletskii, Alexander Kalyuzhnyi

Methods Funct. Anal. Topology **12** (2006), no. 4, 341-352

We prove that the natural action of permutations in a tensor product of type $\mathrm{II}$ factors is free, and compute the von Neumann trace of the projection onto the space of symmetric and antisymmetric elements respectively. We apply this result to computation of von Neumann dimensions of the spaces of square-integrable harmonic forms ($L^{2}$-Betti numbers) of $N$-point configurations in Riemannian manifolds with infinite discrete groups of isometries.

### Generalized Hilbert bialgebras of compact type and their representations

Yu. A. Chapovsky, A. A. Kalyuzhnyi

Methods Funct. Anal. Topology **11** (2005), no. 3, 222-233

### Conditional expectations on compact quantum groups and new examples of quantum hypergroups

Methods Funct. Anal. Topology **7** (2001), no. 4, 49-68

### Algebras with nonquadratic relations associated with Bessel hypergroups

Methods Funct. Anal. Topology **3** (1997), no. 4, 70-76