Several physicists consider non-Poisson bivectors but still apply Kontsevich formality in order to get deformation quantization type results: see e.g. Szabos's review arxiv.org/pdf/1903.05673.pdf

The result they get is a `non-associative star product’.

What is the algebraic structure that the get, or, how to state correctly the deformation quantization problem in this non-associative and non-Poisson context?

Several physicists consider non-Poisson bivectors but still apply Kontsevich formality in order to get deformation quantization type results: see e.g. Szabos's review An introduction to nonassociative physics.

The result they get is a `non-associative star product’.

What is the algebraic structure that they get, or, how to state correctly the deformation quantization problem in this non-associative and non-Poisson context?

Several physicists now consider non-Poisson bivectors but still apply Maxim’s morphism for deformation quantization.

The result is a `non-associative star product’,

So a deformation as a ________? Algebra.

Several physicists consider non-Poisson bivectors but still apply Kontsevich formality in order to get deformation quantization type results: see e.g. Szabos's review arxiv.org/pdf/1903.05673.pdf

The result they get is a `non-associative star product’.

What is the algebraic structure that the get, or, how to state correctly the deformation quantization problem in this non-associative and non-Poisson context?