This paper solves a natural but still open question: can Abstract Categorial Grammars (ACGs) respresent usual categorial grammars? Despite their name and their claim to be a unifying framework, up to now there was no faithful representation of usual categorial grammars in ACGs. This paper shows that Non-Associative Lambek grammars as well as their derivations can be defined using ACGs of order ...

This paper argues that an interlingual representation must explicitly represent some parts of the meaning of a situation as possibilities (or preferences), not as necessary or definite components of meaning (or constraints). Possibilities enable the analysis and generation of nuance, something required for faithful translation. Furthermore, the representation of the meaning of words is crucial,...

The quantum permutation group of the set Xn = {1, . . . , n} corresponds to the Hopf algebra Aaut(Xn). This is an algebra constructed with generators and relations, known to be isomorphic to C(Sn) for n ≤ 3, and to be infinite dimensional for n ≥ 4. In this paper we find an explicit representation of the algebra Aaut(Xn), related to Clifford algebras. For n = 4 the representation is faithful in...

If a group G has a maximal subgroup H, tl-.en G acts by right multiplication on the set fi of right cosets of H in G as a primitive, but not necessarily faithful, permutation group. As part of the search for new finite simple groups it is of interest to determine all possible groups G, and in particular all simple groups, which contain a given group H as a maximal subgroup. This problem is very...

Let [Formula: see text] be a graph manifold containing single JSJ torus and whose blocks are of the form text], where is compact orientable surface with boundary. We show that if does not admit Riemannian metric everywhere nonpositive sectional curvature, then there an essential curve on such any finite-dimensional linear representation maps element representing to matrix all eigenvalues roots ...

We construct an action of the Thompson group $F$ on a compact space built from pairs infinite, binary rooted trees. The arises as $F$-equivariant compactification by translations one its homogeneous spaces, $F/H_2$, corresponding to certain subgroup $H_2$ $F$. representation Hilbert $\ell^2(F/H_2)$ is faithful complex algebra $\mathbb{C}[F]$.

We define a family of braid group representations via the action R-matrix (of quasitriangular extension) restricted quantum $\mathfrak {sl}(2)$ on tensor power simple projective module. This is an extension Lawrence representation specialized at roots unity. Although center has finite order representations, this faithful for our extension.

We show that a $$\mathop {\mathrm {PU}}(1,1)$$ -representation of the hyperelliptic group $$H_n$$ is basic if and only it discrete faithful, thus partially proving conjecture by S. Anan’in (A view on Teichmuller space. II, 2009. arXiv:0709.1711 ) E. Bento Gonçalves I, 2007. arXiv:0907.1633 in case Poincaré disc.

This paper explains the trade-offs between relevance and faithful representation of accounting information analyzed in contexts cash-basis, accrual-basis, fair value methods used to prepare financial statements for Generally Accepted Accounting Principles (GAAP) tax reporting. Discussion role is generally separate from any discussion methods, different needs priorities users GAAP reporting info...