منابع مشابه
Formalizing Complex Plane Geometry
Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and Möbius transformations). In this paper we treat the geometry of c...
متن کاملDifferential Geometry of the q-plane
Hopf algebra structure on the differential algebra of the extended q-plane is defined. An algebra of forms which is obtained from the generators of the extended q-plane is introduced and its Hopf algebra structure is given. E-mail: [email protected] E-mail: [email protected]
متن کاملContributions to differential geometry of spacelike curves in Lorentzian plane L2
In this work, first the differential equation characterizing position vector of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the special curves mentioned above are studied in Lorentzian plane $mathbb{L}%^{2}.$ Finally some characterizations of these special curves are given in $mathbb{L}^{2}.$
متن کاملZ3-graded differential geometry of quantum plane
In this work, the Z3-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given. E-mail: [email protected]
متن کاملDifferential Geometry of the Lie algebra of the quantum plane
We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator x is invertible and furthermore working polynomials in ln x instead of polynomials in x. We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual Hopf algebra.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1922
ISSN: 0002-9947
DOI: 10.2307/1988937