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Everything about Super vector space
Graded vector space with applications to theoretical physics
In mathematics, a super vector space is a -graded vector space, that is, a vector space over a field with a given decomposition of subspaces of grade and grade. The study of super vector spaces and their generalizations is sometimes called super linear algebra. These objects find their principal application in theoretical physics where they are used to describe the various algebraic aspects of supersymmetry. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Super vector spaceA 5-minute orientation
- Skim a recent paper: Enhancing the power quality of dual rotor wind turbines using improved fuzzy space vector modulation and super twisting sliding techniquesInfluential work since 2022
- Pick up a classic book: String-Math 2012The most-reprinted book on the subject
- Read the landmark paper: STSRNet: Deep Joint Space–Time Super-Resolution for Vector Field VisualizationCited 16 times
- Go sideways: SuperalgebraA closely related topic
- Go sideways: Lie superalgebraA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
STSRNet: Deep Joint Space–Time Super-Resolution for Vector Field Visualization
The super order dual of an ordered vector space and the Riesz–Kantorovich formula
Super efficiency and its scalarization in topological vector space
Multiplicity-free Super Vector Spaces
🆕 Influential since 2022
đź“š Books worth reading
- 📕String-Math 2012Germany) String-Math (Conference) (2012 Bonn · 2015
- 📕Quiver Representations and Quiver VarietiesAlexander Kirillov · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Superalgebra In mathematics and theoretical physics, a superalgebra is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra. That is, it is an algebra over a commutative…
- Lie superalgebra In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ‑grading. Lie superalgeb…
- Triple system In algebra, a triple system (or ternar) is a vector space V over a field F together with a F-trilinear map ( ⋅ , ⋅ , ⋅ ) : V × V × V → V . {\displaystyle…
- Representation theory of finite groups The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations…
- Schur–Weyl duality Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear…
- Real structure In mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces.…
- Split-biquaternion In mathematics, a split-biquaternion is a hypercomplex number of the form q = w + x i + y j + z k , {\displaystyle q=w+x\mathrm {i} +y\mathrm {j} +z\mathrm…
- Lie algebra representation In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as…