Superalgebra - Wikipedia
In mathematics and theoretical physics, a superalgebra is a Z 2-graded algebra. [1] That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.
Superalgebra - Encyclopedia of Mathematics
2020年3月31日 · The definition of a superalgebra can be generalized to include the case where the domain of scalars is an arbitrary commutative associative superalgebra $ C $. Examples of associative superalgebras over $ C $ are: the algebra $ …
Introduction to Superalgebra - SpringerLink
Here we lay out the principal facts about supermanifolds, spaces on which some of the coordinate functions commute and the others anti-commute.
We start by introducing the basic notions and definitions in the theory of Lie su-peralgebras, such as basic and queer Lie superalgebras, Cartan and Borel subal-gebras, root systems, positive and fundamental systems. We formulate the main structure results for the basic Lie superalgebras and the queer Lie superalgebras.
INTRODUCTION TO SUPERALGEBRA This chapter contains preparatory information for the following ones. Here we layout the principal facts about supermanifolds, spaces on which some of the coordinate functions commute and the others anti-commute. Recently it has be come dear that the whole apparatus of commutative algebra, of the theory of Lie
Superalgebra - an overview | ScienceDirect Topics
A “superalgebra” is a super vector space A = A 0 ⊕ A 1 which is also an algebra which satisfies A i A j ⊂ A i+j. (ii) The superalgebra is “supercommutative” if, for all homogeneous a, b in A, ab = (− 1) (|a||b|) ba.
super algebra in nLab
2024年8月31日 · In the general sense, superalgebra is the study of algebra. internal to the symmetric monoidal category of ℤ 2 \mathbb{Z}_2-graded vector spaces (super vector spaces); equivalently. over the base topos on superpoints. More specifically, a supercommutative superalgebra is an commutative algebra in the context of superalgebra.
Lemma 1.5. gl(m|n) and sl(m|n) (Except (m, n) = (1, 1), (2, 1)) are basic lie superalgebras meaning that they admit non-degenerate even supersymmetric bilinear forms. Proof. a, b = str(ab) does the trick. Call this the supertrace form. Definition 1.6.
Why are superalgebras so important? - Mathematics Stack Exchange
I know that a superalgebra is a Z/2Z Z / 2 Z -graded algebra and that it behaves nicely. I know very little physics though, so even though I know that the super- prefix is related to supersymmetry, I don't know what that means; is there a compelling mathematical reason to consider superalgebras? Sure: cohomology rings are superalgebras.
What is a Superalgebra | Department of Mathematics
2012年2月9日 · we will discuss the analogous algebraic question: What is a Superalgebra? We will start with basic definitions and examples, and then focus in particular on Lie Superalgebras and their connections to other areas of mathematics.