Related papers: Orthogonal matrix invariants
The algebra of invariants of several 3 x 3 matrices under the action of the orthogonal group by simultaneous conjugation is considered over a field of characteristic different from two. The maximal degree of elements of minimal system of…
The algebra of invariants of d-tuples of n x n skew-symmetric matrices under the action of the orthogonal group by simultaneous conjugation is considered over an infinite field of characteristic different from two. For n=3 and d>0 a minimal…
We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…
We study the structure of the algebra of polynomial invariants for the usual conjugation action of the complex special, SO_n, and general, O_n, orthogonal group on the space of traceless n by n complex matrices. (Note that these two…
We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the…
A linear group G<GL(n) acts on d-tuples of n x n matrices by simultaneous conjugation. In [Adv. Math. 19 (1976), 306-381] Procesi established generators and relations between them for G-invariants, where G is GL(n), O(n), and Sp(n) and the…
Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $GL_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of…
We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…
Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating…
The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariant polynomials. A spanning set of this algebra is in bijective correspondence to a set of…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
Special orthogonal matrices with rational elements form the group SO(n,Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for…
Let R_{n,d} be the ring of invariants of d-tuples of n x n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters for R_{3,3} are determined.…
We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…
A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…
A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary characteristic
Let $p$ be an odd prime and $\mathbb{F}_p$ be the prime field of order $p$. Consider a $2$-dimensional orthogonal group $G$ over $\mathbb{F}_p$ acting on the standard representation $V$ and the dual space $V^*$. We compute the invariant…
The algebra of ${\rm GL}_n$-invariants of $m$-tuples of $n\times n$ matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators…
In this article, we construct a generating set of rational invariants for the action of the orthogonal group $\text{O}(n)$ on the space $\mathbb{R}[x_1,\dots,x_n]_{2d}$ of real homogeneous polynomials of even degree $2d$. This generalizes a…
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x^3=0 is…