# Emergent algebras as generalizations of differentiable algebras, with applications

@inproceedings{Buliga2009EmergentAA, title={Emergent algebras as generalizations of differentiable algebras, with applications}, author={Marius Buliga}, year={2009} }

We propose a generalization of differentiable algebras, where the underlying differential structure is replaced by a uniform idempotent right quasigroup (irq). Algebraically, irqs are related with racks and quandles, which appear in knot theory (the axioms of a irq correspond to the first two Reidemeister moves). An emergent algebra is a algebra A over the uniform irq X such that all operations and algebraic relations from A can be constructed or deduced from combinations of operations in the… Expand

#### 10 Citations

Uniform refinements, topological derivative and a differentiation theorem in metric spaces

- Mathematics
- 2009

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger… Expand

Deformations of normed groupoids and differential calculus. First part

- Mathematics
- 2009

Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $\delta$-structures. Algebraic study of normed groups endowed with dilatation structures is… Expand

Braided spaces with dilations and sub-riemannian symmetric spaces

- Mathematics
- 2010

Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian… Expand

Maps of metric spaces

- Mathematics
- 2011

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive… Expand

How to add space to computation? A tangle formalism for chora and difference

- Mathematics
- 2011

2 From maps to dilation structures 5 2.1 Accuracy, precision, resolution, Gromov-Hausdorff distance . . . 6 2.2 Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Scale… Expand

Computing with space: a tangle formalism for chora and difference

- Computer Science, Physics
- ArXiv
- 2011

Here, inspired by Bateson, the point of view that there is no difference between the map and the territory, but instead the transformation of one into another can be understood by using a formalism of tangle diagrams is explored. Expand

What is a space? Computations in emergent algebras and the front end visual system

- Mathematics, Computer Science
- ArXiv
- 2010

With the help of link diagrams with decorated crossings, I explain computations in emergent algebras, introduced in arXiv:0907.1520, as the kind of computations done in the front end visual system.

More than discrete or continuous: a bird's view

- Mathematics, Biology
- 2010

I try to give mathematical evidence to the following equivalence, which is based on ideas from Plato (Timaeus): reality emerges from a more primitive, non-geometrical, reality in the same way as the brain construct the image of reality, starting from intensive properties. Expand

Normed groupoids with dilations

- Mathematics
- 2011

We study normed groupoids with dilations and their induced deformations. 1 Normed groupoids 2 1.1 Groupoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2… Expand

Introduction to metric spaces with dilations

- Mathematics
- 2010

This paper gives a short introduction into the metric theory of spaces with dilations.

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