Orthogonal and Symplectic Clifford Algebras

Spinor Structures

Orthogonal and Symplectic Geometries.
Tensor Algebras, Exterior Algebras and Symmetric Algebras.
Orthogonal Clifford Algebras.
The Clifford Groups, the Twisted Clifford Groups and Their Fundamental Subgroups.
Spinors and Spin Representations.
Fundamental Lie Algebras and Lie Groups in the Clifford Algebras.
The Matrix Approach to Spinors in Three and Four-Dimensional Spaces.
The Spinors in Maximal Index and Even Dimension.
The Spinors in Maximal Index and Odd Dimension.
The Hermitian Structure on the Space of Complex Spinors—Conjugations and Related Notions.
Spinoriality Groups.
Coverings of the Complete Conformal Group—Twistors.
The Triality Principle, the Interaction Principle and Orthosymplectic Graded Lie Algebras.
The Clifford Algebra and the Clifford Bundle of a Pseudo-Riemannian Manifold. Existence Conditions for Spinor Structures.
Spin Derivations.
The Dirac Equation.
Symplectic Clifford Algebras and Associated Groups.
Symplectic Spinor Bundles—The Maslov Index.
Algebra Deformations on Symplectic Manifolds.
The Primitive Idempotents of the Clifford Algebras and the Amorphic Spinor Fiber Bundles.
Self-Dual Yang-Mills Fields and the Penrose Transform in the Spinor Context.
Symplectic Structures, Complex, Structures, Symplectic Spinors and the Fourier Transform.