Semigroups, Algebras and Operator Theory: ICSAOT 2022, CUSAT, India, March 28–31 (Springer Proceedings in Mathematics & Statistics, 436)

Preface
Acknowledgements
Contents
Contributors
Semigroups
Cross-Connections in Clifford Semigroups
	1 Introduction
	2 Normal Categories and Cross-Connections in Clifford Semigroups
	3 Cross-Connections of a Semilattice
	References
Non-commutative Stone Duality
	1 Introduction
	2 Classical Stone Duality
		2.1 Boolean Algebras
		2.2 Finite Boolean Algebras
		2.3 Arbitrary Boolean Algebras
		2.4 Generalized Boolean Algebras
	3 Boolean Inverse Semigroups
	4 Boolean Groupoids
	5 From Boolean Groupoids to Boolean Inverse Semigroups
	6 From Boolean Inverse Semigroups to Boolean Groupoids
	7 Non-commutative Stone Duality
		7.1 Properties of Prime Filters
		7.2 Properties of Compact-Open Local Bisections
		7.3 Proof of the First Part of the Main Theorem
		7.4 Proof of the Main Theorem
	8 Special Cases
	9 Unitization
	10 Final Remarks
	References
Group Lattices Over Division Rings
	1 Introduction
	2 Group Lattices
	3 G-Lattices Over a Division Ring
	4 Schreier Extension and Associated Group Lattices
	References
Identities in Twisted Brauer Monoids
	1 Introduction
	2 Twisted Brauer Monoids
		2.1 Definition
		2.2 Background
		2.3 Presentation for script upper B Subscript n Superscript taumathcalBτn
		2.4 The Monoid script upper B Subscript n Superscript plus or minus taumathcalBpmτn and its Identities
		2.5 Structure Properties of the Monoid script upper B Subscript n Superscript plus or minus taumathcalBpmτn
	3 Reduction Theorem for Identity Checking
	4 Co-NP-Completeness of Identity Checking in script upper B Subscript n Superscript taumathcalBτn with n greater than or equals 5nge5
	5 Related Results and Further Work
		5.1 Checking Identities in Twisted Partition Monoids
		5.2 Open Questions
	References
Structure of the Semi-group of Regular Probability Measures on Locally Compact Hausdorff Topological Semiroups
	1 Introduction
	2 Preliminaries
	3 Regularity Question
	4 Identification of Elements in upper P left parenthesis upper G right parenthesisP(G) Which Are Algebraically Regular/Not Regular
	5 Probability Measures on Stochastic/Doubly Stochastic Matrices
	6 Concluding Remarks
	References
Compatible and Discrete Normal Categories
	1 Introduction
	2 Preliminaries
		2.1 Categories
		2.2 Normal Categories
		2.3 Normal Duals and Cross Connections
		2.4 Category of Principal Left Ideals of a Regular Semigroup
	3 Compatible and Discrete Normal Categories
		3.1 Compatible Duals
	References
A Range of the Multidimensional Permanent on (0, 1)-Matrices
	1 Introduction and Main Definitions
	2 Preliminaries
	3 Resembling Matrices
	4 Increasing the Dimension
	5 Increasing of Dimension and Consecutive Values of Permanent
	References
Generalized Essential Submodule Graph of an upper RR-module
	1 Introduction and Preliminaries
	2 Generalized Essential Submodule Graph
	3 Conclusion
	References
Algebras
On Category of Lie Algebras
	1 Introduction
	2 Preliminaries
	3 Group Lie Algebras and Plesken Lie Algebras
	4 Category of Lie Algebras
	References
On Lattice Vector Spaces over a Distributive Lattice
	1 Introduction
	2 Lattice Vector Spaces
	3 Congruence Relation and Linear Transformations on l.v.s.
	4 Conclusion
	References
Operator Theory
Application of Geometric Algebra to Koga\'s Work on Quantum Mechanics
	1 Introduction
	2 Fundamentals of Geometric Algebra
		2.1 Tensor Product
	3 The Four-Dimensional Gradient
	4 The Dirac-Hestenes Equation
	5 A Solution to the Dirac-Hestenes Equation
	References
Resolvent Algebra in Fock-Bargmann Representation
	1 Introduction
	2 CCR and Resolvent Algebra
	3 Fock-Bargmann Space and Toeplitz Operators
	4 Resolvent Algebra in Fock-Bargmann Representation
		4.1 Correspondence Theory in the Fock-Bargmann Space
		4.2 Computing script upper D 0 Superscript bold tmathcalD0t
	5 Infinite Dimensional Symplectic Space
	References
left parenthesis n comma epsilon right parenthesis(n,ε)-Condition Spectrum of Operator Pencils
	1 Introduction
	2 On Some Properties of left parenthesis n comma epsilon right parenthesis(n,ε)-Condition Spectrum of Operator Pencils
	3 left parenthesis n comma backslash e right parenthesis(n,ε)-Condition Spectral Mapping Theorem
	4 Stability Analysis of Operator Equations Using left parenthesis n comma backslash e right parenthesis(n,ε)-Condition Spectrum
	References
Numerical Solution of One-Dimensional Hyperbolic Telegraph Equation Using Collocation of Cubic B-Splines
	1 Introduction
	2 Cubic Splines and Boundary Modification
	3 B-Spline Collocation
	4 Convergence Analysis of the Numerical Scheme
	5 Stability Analysis
		5.1 Stability of the Proposed Method
	6 Numerical Experiments
	7 Discussion
	References