Related papers: A computability-theoretic reformulation of the Con…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras…
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
We investigate different notions of "computable topological base" for represented spaces. We show that several non-equivalent notions of bases become equivalent when we consider computably enumerable bases. This indicates the existence of a…
We introduce and investigate different definitions of effective amenability, in terms of computability of F{\o}lner sets, Reiter functions, and F{\o}lner functions. As a consequence, we prove that recursively presented amenable groups have…
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
Cylindrical algebraic decomposition (CAD) is an important tool for working with polynomial systems, particularly quantifier elimination. However, it has complexity doubly exponential in the number of variables. The base algorithm can be…
Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell…
We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…
One of our result is that 5 measurable sets in $R^8$ always admit an equipartition by 2 hyperplanes. This is an instance of a general equipartition problem (formulated by B. Gr{\" u}nbaum and H. Hadwiger) which can be reduced to the…
Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
Let $A \subseteq E$ be a given extension of Hopf (respectively Lie) algebras. We answer the \emph{classifying complements problem} (CCP) which consists of describing and classifying all complements of $A$ in $E$. If $H$ is a given…
We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a…
We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
On page 43 in \cite{Po83} Sorin Popa asked whether the following property holds: \emph{If $\omega$ is a free ultrafilter on $\mathbb N$ and $\mathcal R_1\subseteq \mathcal R$ is an irreducible inclusion of hyperfinite II$_1$ factors such…
We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…
In this paper we shall relate computational complexity to the principle of natural selection. We shall do this by giving a philosophical account of complexity versus universality. It seems sustainable to equate universal systems to complex…