Exponential Maps: Properties and Applications in Lie Groups

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Complete Reducibility of Complex Representations

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Hilpot Liegr: Understanding Nilpotent Lie Groups

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Nilpotent Lie Groups

Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Symmetry in Quantum Field Theory

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.