scholarly journals BRST-Invariant Algebra of Constraints in Terms of Commutators and Quantum Antibrackets

2004 ◽  
Vol 138 (1) ◽  
pp. 1-17 ◽  
Author(s):  
I. A. Batalin ◽  
I. V. Tyutin
Keyword(s):  
Invariant Algebra

scholarly journals On Certain Equations to the Cubic Surface, with Extensions to Higher Space

1934 ◽  
Vol 4 (1) ◽  
pp. 1-11
Author(s):  
W. Saddler
Keyword(s):  
The Other ◽  
Cubic Surface ◽  
Invariant Algebra ◽  
Quadric Cone

The Cubic Surface, as is well known, can be formulated as the locus of a point which, when joined to six given lines—one of which cuts the other five—forms planes enveloping a quadric cone.1 It might be of some interest to show how such a definition leads to one or two of the better known forms of the equation to the surface. The method of approach is by means of the Clebsch Transformation Principle in Geometry and the use of general coordinates. In particular, compound symbols and bracket factors, as developed by H. W. Turnbull2 in his works on Geometry and Invariant Algebra, have been largely used.

Differential Invariants of the (2+1)-Dimensional Breaking Soliton Equation

2016 ◽  
Vol 71 (9) ◽  
pp. 855-862
Author(s):  
Zhong Han ◽  
Yong Chen
Keyword(s):  
Recurrence Relations ◽  
Differential Invariant ◽  
Lie Symmetry ◽  
Differential Invariants ◽  
Moving Frame ◽  
Moving Frames ◽  
Soliton Equation ◽  
Invariant Algebra ◽  
Equivariant Moving Frames

AbstractWe construct the differential invariants of Lie symmetry pseudogroups of the (2+1)-dimensional breaking soliton equation and analyze the structure of the induced differential invariant algebra. Their syzygies and recurrence relations are classified. In addition, a moving frame and the invariantization of the breaking soliton equation are also presented. The algorithms are based on the method of equivariant moving frames.

scholarly journals On the Popov–Pommerening conjecture for linear algebraic groups

2017 ◽  
Vol 154 (1) ◽  
pp. 36-79
Author(s):  
Gergely Bérczi
Keyword(s):  
Characteristic Zero ◽  
Maximal Torus ◽  
Algebraic Groups ◽  
Reductive Group ◽  
Affirmative Answer ◽  
Classical Groups ◽  
Finitely Generated ◽  
Linear Algebraic Groups ◽  
Invariant Algebra

Let $G$ be a reductive group over an algebraically closed subfield $k$ of $\mathbb{C}$ of characteristic zero, $H\subseteq G$ an observable subgroup normalised by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. Popov and Pommerening conjectured in the late 1970s that the invariant algebra $k[X]^{H}$ is finitely generated. We prove the conjecture for: (1) subgroups of $\operatorname{SL}_{n}(k)$ closed under left (or right) Borel action and for: (2) a class of Borel regular subgroups of classical groups. We give a partial affirmative answer to the conjecture for general regular subgroups of $\operatorname{SL}_{n}(k)$.

ADDITIONAL SUPERCONFORMAL ALGEBRAS IN TWO DIMENSIONS

1995 ◽  
Vol 10 (07) ◽  
pp. 567-573
Author(s):  
S. A. APIKYAN
Keyword(s):  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensions ◽  
Superconformal Symmetry ◽  
Invariant Algebra

An SO (N)-invariant algebra of extended superconformal symmetry is obtained in two dimensions with an arbitrary central charge, which besides the energy-momentum tensor contains the currents of 1/2, 1 and 3/2 dimensions.

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