macbook air USB-A to HDMI

Try Amazon.com.

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Thank you for your understanding and support.

Apple offers Thunderbolt and here technically mini DisplayPort to HDMI adapters.

Search for HDMI here: MacBook Air (11-inch, Mid 2013) - Technical Specifications

StarTech has some USB3 adapters that can then connect to a monitor

            USB 3.0 to HDMI         - 1920x1200 (USB32HDPRO) (I've seen this working)

            USB 3.0 to DisplayPort  - 4K 60Hz   (USB32DP24K60) (Dual Monitor)
            USB 3.0 to HDMI Adapter - 4K 30Hz   (USB32HD4K)
            USB 3.0 to DisplayPort  - 4K 30Hz   (USB32DP4K)
            USB 3.0 to DisplayPort  - 2560x1600 (USB32DPPRO)
            USB 3.0 to DVI          - 2048x1152 (USB32DVIPRO)
            USB 3.0 to VGA          - 1920x1200 (USB32VGARO)
            USB 3.0 to VGA          - 1920x1200 (USB32VGARO2)
            USB 3.0 to DVI          - 1920x1200 (USB32DVIPRO2)

You can always get a USB-A to USB-C adapter.