Noncommutative space-time models

Gromov, Nikolay; Kuratov, V. V.

doi:10.1007/s10582-006-0020-y

Cited by 2 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is also a recent interest to this topic in different areas: differential geometry [7,11,12,21,8,2], modal logic [54], quantum mechanics [28,29,57,49], space-time geometry [10,25,26,58,24,22,61], hypercomplex analysis [13,19,20]. A brief history of the topic can be found in [12] and further references are provided in the above papers.…”

Section: Background and Historymentioning

confidence: 99%

Erlangen Program at Large-1: Geometry of Invariants

Kisil¹

2010

SIGMA

View full text Add to dashboard Cite

Abstract. This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL 2 (R) group. We describe here geometries of corresponding domains. The principal rôle is played by Clifford algebras of matching types. In this paper we also generalise the Fillmore-Springer-Cnops construction which describes cycles as points in the extended space. This allows to consider many algebraic and geometric invariants of cycles within the Erlangen program approach.

show abstract

Section: Background and Historymentioning

confidence: 99%

Erlangen Program at Large-1: Geometry of Invariants

Kisil¹

2010

SIGMA

View full text Add to dashboard Cite

show abstract

Induced Representations and Hypercomplex Numbers

Kisil

2012

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

ABSTRACT. In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G = SL 2 (R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional subgroup of SL 2 (R), is a linear-fractional transformation on hypercomplex numbers. Thus, we investigate various hypercomplex characters of subgroups H. The correspondence between the structure of the group SL 2 (R) and hypercomplex numbers can be illustrated in many other situations as well. We give examples of induced representations of SL 2 (R) on spaces of hypercomplex valued functions, which are unitary in some sense. Raising/lowering operators for various subgroup prompt hypercomplex coefficients as well.

show abstract

Noncommutative space-time models

Cited by 2 publications

References 7 publications

Erlangen Program at Large-1: Geometry of Invariants

Erlangen Program at Large-1: Geometry of Invariants

Induced Representations and Hypercomplex Numbers

Contact Info

Product

Resources

About