We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra. •The quantization procedure, the quantizer-dequantizer method, and star-product technique are considered to construct associative products and the associative algebras formed by the quantizer-dequantizer operators and their symbols.•The corresponding Lie algebras are constructed, and the case where the quantizer-dequantizer operators form a self-dual system is considered.•Using tomographic quantizer-dequantizer operators and their symbols, the continuous associative algebra and the corresponding Lie algebra are constructed.