Introduction to Quantum Groups and Algebras in Mathematics
Explore the philosophy of quantum groups, spaces, and algebras in mathematics. Learn about recovering spaces from their algebras, algebras of functions on groups, and the concept of a Hopf algebra. Discover how additional structures on spaces are captured through algebras of functions, and the role
0 views • 14 slides
Algebraic Homomorphisms and Singular Transformations in Mathematics
An exploration of Cayley's theorem analog for groups in algebra, showcasing the isomorphism of algebras with unit elements over fields to subalgebras of some vector space. Additionally, a discussion on characterizing singular transformations in finite-dimensional vector spaces over fields. The expla
0 views • 14 slides
Incorporating General Relativity into Quantum Theory through Riemannian Geometry
Framing Riemannian Geometry as a Generalized Lie Algebra to combine General Relativity with Quantum Theory. The proposal extends Heisenberg Algebra to incorporate a more general geometry, allowing for a function of position in commutator relationships. The discussion covers historical developments,
0 views • 50 slides
Decidability and Extensions of Modal Epistemic Logics
The research delves into the introduction of the new modal epistemic logic E.P, derived from the infinitely valued ukasiewicz logic by incorporating an axiom of the logic P of perfect MV-algebras. The study explores the enrichment of the language with a "quasi-knowledge operator" and establishes the
0 views • 30 slides
Advancing Theoretical Computer Science and Industry Solutions
The Advanced Computing Research Centre (ACRC) led by Prof. Georg Struth and Dr. Anthony Simons focuses on advancing the state-of-the-art in theoretical computer science and applying theoretical results to practical industry solutions. Their work encompasses logic, algebras, formal specification, sof
0 views • 12 slides
Recent Advances in Operator Theory and Operator Algebras
Helly's theorem on intersection of balls, Jung's constant, and Banach spaces properties are explored in this study on operator theory and algebras. The relationship between 1-injective Banach spaces and intersection properties of balls is discussed, providing valuable insights for mathematical appli
0 views • 26 slides
Exceptional G(2) Extension from Cayley Dickson Algebras Automorphism Groups
Explore the exceptional G(2) extension of the Standard Model through Cayley Dickson algebras, delve into the automorphism search, and discover the potential of strong sector gauge theories broken by additional Higgs mechanisms. Unveil the exotic bosonic content and delve into the realms of dark matt
0 views • 13 slides
Lie Algebras in Physics: Geometric Applications and Non-Compact Groups
Explore the fascinating world of Lie algebras in physics, delving into geometric and non-compact groups, Conservation Laws, Noether's theorem, and the symmetries they reveal. Discover the classification of Lie algebras with Dynkin diagrams, Infinite families, and Exceptional cases. Dive into the com
0 views • 13 slides