相关论文: Generators of algebraic curvature tensors based on…

We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the…

The background of this paper is the following: search of the minimal systems of generators for this class of group which still was not founded also problem of representation for this class of group, exploration of systems of generators for…

For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in…

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one…

The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie…

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity…

In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…

In a previous paper, we proposed a construction of $U_q(sl(2))$ quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works.…

A gauge theory with an underlying SU_q(2) quantum group symmetry is introduced, and its properties examined. With suitable assumptions, this model is found to have many similarities with the usual SU(2)\times U(1) Standard Model,…

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…

Let S be a smooth cubic surface over a field K. It is well-known that new K-rational points may be obtained from old ones by secant and tangent constructions. A Mordell-Weil generating set is a subset B of S(K) of minimal cardinality which…

We consider the class of finitely generated groups whose relators are powers of commutators of the generators. This class contains as a small subclass graph groups (also called RAAGs), namely if all powers are one. Graph groups are the only…

For any ring $R$, we introduce an invariant in the form of a partially ordered abelian semigroup $\mathrm{S}(R)$ built from an equivalence relation on the class of countably generated projective modules. We call $\mathrm{S}(R)$ the Cuntz…

We develop invariant theory for the quantum group ${\rm U}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal A}_m$ be the braided symmetric algebra over $m$-copies of the $7$-dimensional simple ${\rm…

The supermembrane in light-cone gauge gives rise to a supersymmetric quantum mechanics system with SU(N) gauge symmetry when the group of area preserving diffeomorphisms is suitably regulated. de Wit, Marquard and Nicolai showed how…

A finite $W$-algebra $U(\g,e)$ is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\g$. It is possible…

$U(N)^{\otimes r} \otimes O(N)^{\otimes q}$ invariants are constructed by contractions of complex tensors of order $r+q$, also denoted $(r,q)$. These tensors transform under $r$ fundamental representations of the unitary group $U(N)$ and…

We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2)…

We consider the reflection equation algebra for a finite dimensional R-matrix for the $(h,w)$-deformed Heisenberg algebra ${\cal U}_{h,w}(h(4))$. A representation of the reflection matrix $K$ is constructed using the matrix generators…

The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same degree determine a gradation of the Clifford algebra. Through these…