scholarly journals Algebraic duality of constant algebras

1999 ◽  
Vol 49 (2) ◽  
pp. 415-420
Author(s):  
I. Chajda ◽  
R. Halaš ◽  
A. G. Pinus
Keyword(s):  
Algebraic Duality

scholarly journals AN ALGEBRAIC DUALITY THEORY FOR MULTIPLICATIVE UNITARIES

2001 ◽  
Vol 12 (04) ◽  
pp. 415-459 ◽  
Author(s):  
SERGIO DOPLICHER ◽  
CLAUDIA PINZARI ◽  
JOHN E. ROBERTS
Keyword(s):  
Hilbert Spaces ◽  
Duality Theory ◽  
Duality Theorem ◽  
Separable Hilbert Space ◽  
Regular Representation ◽  
Cuntz Algebra ◽  
Relative Depth ◽  
Minimal Representation ◽  
C Algebras ◽  
Algebraic Duality

Multiplicative unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki–Tatsuuma Duality Theorem characterizes abstractly C*-algebras acted on by unital endomorphisms that are intrinsically related to the regular representation of a multiplicative unitary. The relevant C*-algebras turn out to be simple and indeed separable if the corresponding multiplicative unitaries act on a separable Hilbert space. A categorical analogue provides internal characterizations of minimal representation categories of a multiplicative unitary. Endomorphisms of the Cuntz algebra related algebraically to the grading are discussed as is the notion of braided symmetry in a tensor C*-category.

scholarly journals Applications of algebraic duality to group divisible structures

1981 ◽  
Vol 37 (2-3) ◽  
pp. 159-166 ◽  
Author(s):  
Bhagwandas ◽  
W.G. Bridges
Keyword(s):  
Group Divisible ◽  
Algebraic Duality

scholarly journals The exponential-dual matrix method: Applications to Markov chain analysis

2021 ◽  
pp. 217-235
Author(s):  
Gerardo Rubino ◽  
Alan Krinik
Keyword(s):  
Queueing Theory ◽  
Matrix Method ◽  
Arbitrary Point ◽  
Stable Model ◽  
Transient Phase ◽  
State Distribution ◽  
Chain Analysis ◽  
Stochastic Duality ◽  
Linear Differential ◽  
Algebraic Duality

Classic performance evaluation using queueing theory is usually done assuming a stable model in equilibrium. However, there are situations where we are interested in the transient phase. In this case, the main metrics are built around the model’s state distribution at an arbitrary point in time. In dependability, a significant part of the analysis is done in the transient phase. In previous work, we developed an approach to derive distributions of some continuous time Markovian models, built around uniformization (also called Jensen’s method), transforming the problem into a discrete time one, and the concept of stochastic duality. This combination of tools provides significant simplifications in many cases. However, stochastic duality does not always exist. Recently, we discovered that an idea of algebraic duality, formally similar to stochastic duality, can be defined and applied to any linear differential system (or equivalently, to any matrix). In this case, there is no limitation, the transformation is always possible. We call it the exponential-dual matrix method. In the article, we describe the limitations of stochastic duality and how the exponential-dual matrix method operates for any system, stochastic or not. These concepts are illustrated throughout our article with specific examples, including the case of infinite matrices.

scholarly journals Min algebraic duality

1987 ◽  
Vol 16 (1) ◽  
pp. 87-90
Author(s):  
Donna Crystal Llewellyn
Keyword(s):  
Algebraic Duality

Adler's principle and algebraic duality

1973 ◽  
Vol 15 (2) ◽  
pp. 495-504 ◽  
Author(s):  
D. V. Volkov ◽  
V. D. Gershun ◽  
A. A. Zheltukhin ◽  
A. I. Pashnev
Keyword(s):  
Algebraic Duality
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