Formal languages | Algebraic structures | Algebraic logic

In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to the former, while adding the left and right residuation or implication operations of the former to the latter. Unlike dynamic logic and other modal logics of programs, for which programs and propositions form two distinct sorts, action algebra combines the two into a single sort. It can be thought of as a variant of intuitionistic logic with star and with a noncommutative conjunction whose identity need not be the top element. Unlike Kleene algebras, action algebras form a variety, which furthermore is finitely axiomatizable, the crucial axiom being a•(a → a)* ≤ a. Unlike models of the equational theory of Kleene algebras (the regular expression equations), the star operation of action algebras is reflexive transitive closure in every model of the equations. (Wikipedia).

Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

16 You have made it to the first exciting video Operations

To be honest, the topics have been very dry up to now. Here is the first bit of excitement. Operations. Understanding operations is a fundamental priority in abstract algebra.

From playlist Abstract algebra

The inverse of a matrix -- Elementary Linear Algebra

This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.

From playlist Elementary Linear Algebra

Abstract Algebra: Group actions are defined as a formal mechanism that describes symmetries of a set X. A given group action defines an equivalence relation, which in turn yields a partition of X into orbits. Orbits are also described as cosets of the group. U.Reddit course materials a

From playlist Abstract Algebra

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In this first video on group actions, I use an example of some previous work on the symmetric group to give you some intuition about group actions. Beware when reading your textbook. It is probably unnecessary difficult just due to the dot notation that is used when describing group acti

From playlist Abstract algebra

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In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

Group Definition (expanded) - Abstract Algebra

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin

From playlist Abstract Algebra

Linear Equations from the Graph of the Line, No. 1

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From playlist Algebra; Linear Equations

Field Definition (expanded) - Abstract Algebra

The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They

From playlist Abstract Algebra

Rigidity for von Neumann algebras – Adrian Ioana – ICM2018

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From playlist Analysis & Operator Algebras

Eusebio Gardella: "Crossed products by partial actions"

Actions of Tensor Categories on C*-algebras 2021 "Crossed products by partial actions" Eusebio Gardella - Westfälische Wilhelms Universität Münster Institute for Pure and Applied Mathematics, UCLA January 27, 2021 For more information: https://www.ipam.ucla.edu/atc2021

From playlist Actions of Tensor Categories on C*-algebras 2021

Ralf Meyer: On the classification of group actions on C*-algebras up to equivariant KK-equivalence

Talk by Ralf Meyer in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 10, 2020.

From playlist Global Noncommutative Geometry Seminar (Europe)

Alcides Buss: Amenable actions of groups on C*-algebras

Talk by Alcides Buss in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/amenable-actions-of-groups-on-c-algebras/ on February 26, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

Corey Jones: "Anomalous symmetries of C*-algebras"

Actions of Tensor Categories on C*-algebras 2021 "Anomalous symmetries of C*-algebras" Corey Jones - North Carolina State University Abstract: A fusion category is called pointed if every simple object is invertible under the monoidal product. These are described by finite groups togethe

From playlist Actions of Tensor Categories on C*-algebras 2021

Symmetries of hamiltonian actions of reductive groups - David Ben-Zvi

Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II - Amnon Ta-Shma Computer Science/Discrete Mathematics Seminar II Topic: Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II Speaker: Amnon Ta-Shma Affiliation: Tel Aviv University Date: January 3

From playlist Mathematics

Gábor Szabó: "Classification of group actions on C*-algebras"

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From playlist Actions of Tensor Categories on C*-algebras 2021

Lecture 10: The circle action on THH

In this video we construct an action of the circle group S^1 = U(1) on the spectrum THH(R). We will see how this is the homotopical generalisation of the Connes operator. The key tool will be Connes' cyclic category. The speaker is of course Achim Krause and not Thomas Nikolaus as falsely

From playlist Topological Cyclic Homology

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From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

Cyril Houdayer: Noncommutative ergodic theory of lattices in higher rank simple algebraic groups

Talk by Cyril Houdayer in the Global Noncommutative Geometry Seminar (Americas) on March 18, 2022. https://globalncgseminar.org/talks/tba-28/

From playlist Global Noncommutative Geometry Seminar (Americas)